Showing papers in "Filomat in 2011"
TL;DR: In this paper, the sequence space lλp of non-absolute BK type was introduced and it was shown that the spaces l and lp are linearly isomorphic for 0 < p ≤ 1 and 1 ≤ p ≤ ∞.
Abstract: In the present paper, we introduce the sequence space lλp of non-absolute
type and prove that the spaces lλp and lp are linearly isomorphic for 0 < p ≤
∞. Further, we show that lλp is a p-normed space and a BK-space in the cases
of 0 < p < 1 and 1 ≤ p ≤ ∞, respectively. Furthermore, we derive some
inclusion relations concerning the space lλp. Finally, we construct the basis
for the space lλp, where 1 ≤ p < ∞.
78 citations
TL;DR: In this paper, the authors apply the deflitions proposed by Ali et al. to the concept of soft sets, which can be seen as an efiective mathematical tool to deal with uncertainties, since it is free from the di‐culties that the usual theoretical approaches have troubled.
Abstract: Molodtsov introduced the theory of soft sets, which can be seen as an efiective mathematical tool to deal with uncertainties, since it is free from the di‐culties that the usual theoretical approaches have troubled. In this paper, we apply the deflnitions proposed by Ali et al. [M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009), 1547{1553] to the concept of soft near
58 citations
TL;DR: In this paper, the setting of generalized metric spaces was used to obtain common fixed point results for three maps, and these results generalize several well known comparable results in the literature.
Abstract: In this paper, we use the setting of generalized metric spaces to obtain common fixed point results for three maps. These results generalize
several well known comparable results in the literature.
50 citations
TL;DR: In this paper, the authors introduced the notion of weak cyclic Kannan contraction and gave some convergence and existence results for best proximity points for weak CK contraction in the setting of a uniformly convex Banach space.
Abstract: In this paper we introduce the notion of weak cyclic Kannan contraction. We give some convergence and existence results for best proximity points for weak cyclic Kannan contractions in the setting of a uniformly convex Banach space.
40 citations
TL;DR: The sum-connectivity index of a simple graph G is deflned in mathematical chemistry as R + (G) = X uv2E(G) (du + dv) i 1=2 as discussed by the authors.
Abstract: The sum-connectivity index of a simple graph G is deflned in mathematical chemistry as R + (G) = X uv2E(G) (du + dv) i 1=2
34 citations
TL;DR: In this article, the authors define statistical convergence and statistical convergence for Cauchy double sequences on intuitionistic fuzzy normed spaces (IFNS in short), where λ = (λn ) and µ = (µm) are two nondecreasing real numbers of positive real numbers such that each tending to ∞ and λn+1 ≤ λ n====== + 1, λ1 = 1.
Abstract: In this paper, we define (λ, µ)- statistical convergence and (λ,
µ)-statistical Cauchy double sequences on intuitionistic fuzzy normed spaces
(IFNS in short), where λ = (λn ) and µ = (µm) be two non-decreasing
sequences of positive real numbers such that each tending to ∞ and λn+1 ≤ λn
+ 1, λ1 = 1; µm+1 ≤ µm + 1, µ1 = 1. We display example that shows our method
of convergence is more general for double sequences in intuitionistic fuzzy
normed spaces.
27 citations
TL;DR: In this paper, the authors prove the logarithmic convexity of the elementary function bx−ax/x, where x ≠ 0 and b > a > 0.
Abstract: In the paper, we first prove the logarithmic convexity of the elementary
function bx−ax/x, where x ≠ 0 and b > a > 0. Basing on this, we then
provide a simple proof for Schur-convex properties of the extended mean
values, and, finally, discover some convexity related to the extended mean
values.
27 citations
TL;DR: In this paper, Bhaskar and Lakshmikantham established several fixed point theorems for mixed monotone mappings in partially ordered metric spaces, which generalize and complement some known results.
Abstract: This paper is concerned with mixed monotone mappings in partially ordered
cone metric spaces We establish several fixed point theorems, which
generalize and complement some known results Especially, even in a partially
ordered metric space, our main results are generalizations of the fixed point
theorems due to Bhaskar and Lakshmikantham [T Grana Bhaskar, V
Lakshmikantham, Fixed point theorems in partially ordered metric spaces and
applications, Nonlinear Anal TMA 65 (2006) 1379-1393]
25 citations
TL;DR: In this paper, the authors obtained multi-valed mapping generalizations of two recent fixed point theorem theorems of Kikkawa and Suzuki, namely, some similarity between contractions and Kannan mappings and main theorem of Enjouji et al.
Abstract: In this paper we obtain multi-valed mapping generalizations of two recent
theorems of Kikkawa and Suzuki [M. Kikkawa and T. Suzuki, Some similarity
between contractions and Kannan mappings, Fixed Point Theory Appl., (2008),
Article ID 649749, 1-8] and the main theorem of Enjouji et all. [Y. Enjouji,
M. Nakanishi and T. Suzuki, A Generalization of Kannan’s Fixed Point Theorem,
Fixed Point Theory and Applications, Volume 2009, Article ID 192872, 10
pages].
25 citations
TL;DR: In this paper, the existence of common flxed points for two weakly compatible mappings satisfying a generalized condition (B) has been proved, which generalizes some theorems of Al-Thagafl and Shahzad [2] and Babu, Sandhya and Kameswari.
Abstract: We prove the existence of common flxed points for two weakly compatible mappings satisfying a ‘generalized condition (B)’. This result generalizes some theorems of Al-Thagafl and Shahzad [2] and Babu, Sandhya and Kameswari [3].
24 citations
TL;DR: In this paper, the authors considered the maximum and minimum for the first reformulated Zagreb index of graphs with connectivity at most k, and the corresponding extremal graphs were characterized.
Abstract: The authors Milicevic et al. introduced the reformulated Zagreb indices
[1], which is a generalization of classical Zagreb indices of chemical graph
theory. In this paper, we mainly consider the maximum and minimum for the
first reformulated index of graphs with connectivity at most k. The
corresponding extremal graphs are characterized.
TL;DR: In this article, Parashar and Choudhary defined certain paranorms in some============ Orlicz sequence spaces of Maddox type and applied them to the topologization of various generalized Orliczi sequence spaces.
Abstract: In 1994 S D Parashar and B Choudhary defined certain paranorms in some
Orlicz sequence spaces of Maddox type Their ideas are applied later by many
authors for topologization of various generalized Orlicz sequence spaces We
determine alternative F-seminorms in such spaces by using the standard
arguments of modular spaces theory and a result about the topologization of
sequence spaces defined by modulus functions
TL;DR: In this paper, a generalized metric space (G-metric space) was used to prove fixed point theorems for mappings with a contractive iterate at a point.
Abstract: Using the setting of generalized metric space, so called G-metric space, a
fixed point theorems for mappings with a contractive iterate at a point are
proved. This result generalize well known comparable result.
TL;DR: Some properties of a semi-symmetric non-metric connection in a Kenmotsu manifold are studied.
Abstract: Yano [1] defined and studied semi-symmetric metric connection in a Riemannian
manifold and this was extended by De and Senguta [8] and many other
geometers. Recently, the present authors [3], [5] defined semi-symmetric
non-metric connections in an almost contact metric manifold. In this paper,
we studied some properties of a semi-symmetric non-metric connection in a
Kenmotsu manifold.
TL;DR: In this article, the maximal function estimates for the commutator associated with some integral operator with general kernel and the weighted Lipschitz functions were established for weighted Lebesgue, Morrey and Triebel-Lizorkin spaces.
Abstract: In this paper, we establish the sharp maximal function estimates for the
commutator associated with some integral operator with general kernel and the
weighted Lipschitz functions. As an application, we obtain the boundedness of
the commutator on weighted Lebesgue, Morrey and Triebel-Lizorkin space. The
operator includes Littlewood-Paley operators, Marcinkiewicz operators and
Bochner-Riesz operator.
TL;DR: In this article, the authors studied the boundedness and compactness of the integral operator Cn φ,g,g which is defined as a self-map of a nonnegative integer.
Abstract: Let g ∈ H(D), n be a nonnegative integer and φ be an analytic self-map of D.
We study the boundedness and compactness of the integral operator Cn φ,g, which
is defined by Cn φ,g f)(z) = ∫z0 f(n)(φ(ξ))g(ξ)dξ, z∈D, f∈H(D), from
QK(p,q) and QK,0(p,q) spaces to α-Bloch spaces and little α-Bloch spaces.
TL;DR: In this article, the stability of the functional equation of a non-empty set with respect to a fixed point theorem of the Ciric type has been analyzed based on the use of fixed point theory.
Abstract: Let S be a non empty set. We prove the stability (in the sense of Ulam) of
the functional equation: f(t)=F(t,f (Φ(t))), where φ is a given function
of S into itself and F is a function satisfying a contraction of Ciric type
([5]). Our analysis is based on the use of a fixed point theorem of Ciric
(see [5] and [4]). In particular our result provides a generalization and a
natural continuation of a paper of Baker (see [3]).
TL;DR: In this article, the general solution and the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary t-norms were obtained.
Abstract: In this paper, we obtain the general solution and the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary t-norms f(x + 3y) + f(x i 3y) = 9(f(x + y) + f(x i y)) i 16f(x):
TL;DR: In this paper, a generalization of the Ostrowski inequality for functions in L p -spaces is introduced and then applied to provide some estimates for the error value of numerical quadrature rules of equal coe−cients type.
Abstract: A new generalization of the Ostrowski inequality for functions in L p -spaces is introduced and then applied to provide some estimates for the error value of numerical quadrature rules of equal coe‐cients type.
TL;DR: In this paper, a generalized countable iterated function system (GCIFS) is proposed to generate fractals by considering contractions from X £ X into X instead of contractions on the metric space X to itself, where (X;d) is a compact metric space.
Abstract: One of the most common and most general way to generate fractals is by using iterated function systems which consists of a flnite or inflnitely many maps. Generalized countable iterated function systems (GCIFS) are a generalization of countable iterated function systems by considering contractions from X £ X into X instead of contractions on the metric space X to itself, where (X;d) is a compact metric space. If all contractions of a GCIFS are Lipschitz with respect to a parameter and the supremum of the Lipschitz constants is flnite, then the associated attractor depends continuously on the respective parameter.
TL;DR: In this article, common flxed point theorems for mappings satisfying a generalized contractive condition are obtained in symmetric spaces by using the notion of common property (E.A.).
Abstract: In this paper, common flxed point theorems for mappings satisfying a generalized contractive condition are obtained in symmetric spaces by using the notion of common property (E.A.). In the process, a host of previously known results are improved and generalized. We also derive results on common flxed point in probabilistic symmetric spaces.
TL;DR: In this article, the concept of statistical limit superior and statistical limit inferior in probabilistic normed spaces is studied and the results are analogous to the results of Fridy and Orhan [Proc. Amer. Math. Soc. Soc., 125, 3625-3631] but proofs are somewhat different and interesting.
Abstract: In this paper we study the concept of statistical limit superior and
statistical limit inferior in probabilistic normed spaces. Our results are
analogous to the results of Fridy and Orhan [Proc. Amer. Math. Soc.
125(1997), 3625-3631] but proofs are somewhat different and interesting. We
also demonstrate through an example how to compute these points in PN-spaces.
TL;DR: In this paper, the authors give some theorems on point of coincidence and common fixed points for two self mappings satisfying some general contractive conditions in vector metric spaces, and generalize some well-known recent results.
Abstract: In this paper we give some theorems on point of coincidence and common fixed
points for two self mappings satisfying some general contractive conditions
in vector metric spaces. Our results generalize some well-known recent
results.
TL;DR: In this paper, the authors established sufficient conditions for the existence of solvable solutions of some differential equation and its solvability in CL, a subset of the Banach space (C [a, b], ||•||).
Abstract: In this paper we shall establish sufficient conditions for the existence of
solutions of some differential equation and its solvability in CL, subset of
the Banach space (C [a, b], ||•||). The main tool used in our study is the
nonexpansive operator technique.
TL;DR: In this paper, the modular sequence space l{Mk,p,q,s,∆n/vm} was generalized by introducing the sequence space mk, p, q, s, n/vm.
Abstract: In this paper we generalize the modular sequence space l{Mk} by introducing
the sequence space l{Mk,p,q,s,∆n/vm}. We give various properties relevant
to algebraic and topological structures of this space and derived some other
spaces.
TL;DR: The notion of quasicontinuity was perhaps the first time used by R. Baire in this paper, where he showed that a topological space with the property QP can be characterized by a trajectory of the form {(xk, fnk (xk )): k∈ω} if and only if we can approach most points along a vertical trajectory.
Abstract: The notion of quasicontinuity was perhaps the first time used by R. Baire in
[2]. Let X, Y be topological spaces and Q(X,Y) be the space of
quasicontinuous mappings from X to Y. If X is a Baire space and Y is
metrizable, in Q(X,Y) we can approach each (x, y) in the graph Grf of f
along some trajectory of the form {(xk, fnk (xk )): k∈ω} if and only if
we can approach most points along a vertical trajectory. This result
generalizes Theorem 5 from [3]. Moreover in the class of topological spaces
with the property QP we give a characterization of Baire spaces by the above
mentioned fact. We also study topological spaces with the property QP.
TL;DR: In this article, the notions of I-Alexandrofi and Ig-aleandrofi ideal topological spaces are introduced and studied, and the characterizations and properties of these ideal spaces are investigated.
Abstract: In this paper, the notions of I-Alexandrofi and Ig-Alexandrofi ideal topological spaces are introduced and studied. Also, characterizations and properties of I-Alexandrofi and Ig-Alexandrofi ideal topological spaces are investigated.
TL;DR: In this article, the authors define the concept of premeager and discuss when a pseudobounded paratopological group is a topological group, and also discuss some properties of ω-pseudobounded topological groups.
Abstract: We say that a paratopological group G is pseudobounded (ω-pseudobounded), if
for every neighborhood V of the identity element e of G, there exists a
natural number n such that G=Vn (G = U∞n=1 Vn). In this paper, we mainly
discuss the pseudobounded and ω-pseudobounded paratopological groups. First,
we give an example to show that a theorem in [4] is not true. And then, we
define the concept of premeager, and discuss when a pseudobounded
paratopological group is a topological group. Moreover, we also discuss some
properties of ω-pseudobounded topological groups, and show that the class of
connected topological groups is contained in the class of ω-pseudobounded
topological groups. Finally, some open problems concerning the
paratopological groups are posed.
TL;DR: In this article, the limit behaviors for the deviation between the p-quantile ξˆnp and ξp by sampling from a sequence of independent and identically distributed samples of size n were discussed.
Abstract: In this article, we discuss the limit behaviors for the deviation between the
sample p-quantile ξˆnp and the p-quantile ξp by sampling from a sequence of
independent and identically distributed samples of size n. The moderate
deviation, large deviation and Bahadur asymptotic efficiency for (ξˆpn−ξp)
are established under some weak conditions.
TL;DR: In this article, a new instability theorem related to a flfth order nonlinear difierential equation with a constant delay is introduced, which is based on the Lyapunov-Krasovskii functional approach.
Abstract: Text of the abstract. The main purpose of this paper is to introduce a new instability theorem related to a flfth order nonlinear difierential equation with a constant delay. By means of the Lyapunov-Krasovskii ([8], [13]) functional approach, we obtain a new result on the topic.