Showing papers in "Filomat in 2008"
TL;DR: In this article, the authors prove a common fixed point theorem in a probabilistic metric space by combining the ideas of pointwise R-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions with an implicit relation.
Abstract: In this paper, we prove a common fixed point theorem in a probabilistic metric space by combining the ideas of pointwise R-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions with an implicit relation. .
30 citations
TL;DR: In this article, the authors prove common fixed point theorems for four mappings satisfying implicit relations in symmetric spaces using the concept of occasionally weakly compatible mappings, which generalize results of [1], [3], [4] and [7].
Abstract: We prove common fixed point theorems for four mappings satisfying implicit relations in symmetric spaces using the concept of occasionally weakly compatible mappings. Our Theorems generalize results of [1], [3], [4] and [7].
22 citations
TL;DR: In this paper, the authors prove a common fixed point theorem for multi-valued mappings under the condition of weak compatibility and define compatible maps of type (I) for multi valued mappings.
Abstract: In this paper, we prove a common fixed point theorem for multi valued mappings under the condition of weak compatibility. Also, we define compatible maps of type (I) for multi valued mappings and prove a common fixed point theorem for this type mappings. We use an implicit relation to prove our main theorems.
15 citations
TL;DR: In this article, the authors investigate properties of a-open sets and e ⁄ -open sets in topological spaces, and show that the properties of open sets depend on the degree of the set.
Abstract: The aim of this paper is to investigate some properties of a-open sets and e ⁄ -open sets in topological spaces.
14 citations
TL;DR: In this article, a weaker version of normality, called …-normality, has been proposed, which is a property which lies between almost normality and normality in topological spaces.
Abstract: A topological space X is called …-normal if for any two disjoint closed subsets A and B of X one of which is …-closed, there exist two open disjoint subsets U and V of X such that A µ U and B µ V . We will present some characterizations of …-normality and some examples to show relations between …-normality and other weaker version of normality such as mild normality, almost normality, and quasi-normality. We investigate in this paper a weaker version of normality called …-normality. We will prove that …-normality is a property which lies between almost normality and normality. We will present some characterizations of …-normality and some examples to show relations between …-normality and other weaker versions of
13 citations
TL;DR: In this article, a common fixed point theorem for multi-valued mappings satisfying an implicit relation on fuzzy metric spaces is given for the special case of mappings that satisfy a relation on a fuzzy metric space.
Abstract: In this paper, we give a common fixed point theorem for multi-valued mappings satisfying an implicit relation on fuzzy metric spaces.
12 citations
TL;DR: In this paper, the star complement technique was used to reprove the result of Wilbrink and Brouwer that the strongly regular graph with parameters (57, 14, 1, 4) does not exist.
Abstract: In this paper we show how the star complement technique can be used to reprove the result of Wilbrink and Brouwer that the strongly regular graph with parameters (57, 14, 1, 4) does not exist. .
10 citations
TL;DR: In this article, a simple proof that convexoid operators on Hilbert space are normaloid is given, and a simple example to show that the converse fails....
Abstract: We offer a simple proof that convexoid operators on Hilbert space are normaloid, and given an example to show that the converse fails. .
10 citations
TL;DR: For ordered sets under anti-orders, this paper showed an isomorphism theorem for strongly extensional and embedding reverse isotone bijections, where the apartness 6Y is tight.
Abstract: In this paper we show some kind of isomorphism theorem for ordered sets under antiorders. Let (X;=X;6X;fi) and (Y;=Y ;6Y ;fl) be ordered sets under antiorders, where the apartness 6Y is tight. If ’ : X i! Y is reverse isotone strongly extensional mapping, then there exists a strongly extensional and embedding reverse isotone bijection
9 citations
TL;DR: In this paper, the S L (¢)-asymptotically equivalence analogues theorems of [5] and [6] were proved using new definitions which are a natural combination of the definition for asymptotic equivalence ¢ilacunary statistically convergence.
Abstract: This paper presents new definitions which are a natural combination of the definition for asymptotically equivalence ¢ilacunary statistically convergence. Using this definitions we have proved the S L (¢)-asymptotically equivalence analogues theorems of [5] and [6].
8 citations
TL;DR: In this paper, the theory of dierential subordination was used to obtain a new condition for star-like functions, defined in the punctured disc and expressed by means of j(1 i fi)zf(z) + z 2 f 0 (z)+ fij, where fi 2 [0;1].
Abstract: In this paper we will use the theory of dierential subordinations to obtain a new condition for meromorphic functions, defined in the punctured disc ˙ U = U n f0g, U = fz 2C : jzj < 1g, which are of the form f(z) = 1 + anz n + an+1z n+1 + :::, to be starlike functions. The new condition for starlikeness is expressed by means of j(1 i fi)zf(z) + z 2 f 0 (z) + fij, where fi 2 [0;1).
TL;DR: In this article, it was shown that there do not exist proper warped product submanifolds of the type N £f NT and NT £f N where NT is an invariant and N is any real non-anti invariant sub manifold of a Kaehler manifold.
Abstract: In this paper we have shown that there do not exist proper warped product submanifolds of the type N £f NT and NT £f N where NT is an invariant and N is any real non-anti invariant submanifold of a Kaehler manifold. We thus generalize the results of B. Sahin [10] who projected same results for a restricted class, the class of warped product submanifolds Nµ £f NT and NT £f Nµ.
TL;DR: In this article, the γ-open sets are defined in terms of a function on a set X defined by a function function on X, and the properties of these subsets are investigated.
Abstract: We consider a collection of subsets of a set X defined in terms of a function on (X); called the γ-open sets, which is not a topology but we show that some of the results established for topologies are valid for this collection. In particular, we define δγ-open sets in a γ-space and characterize its properties. Also, we discuss the properties of γ-rare sets and characterize δγ-open sets in terms of γ-rare sets.
TL;DR: In this article, a stationary bivariate minification process with Marshall and Olkin exponential distribution is presented, where the unknown parameters are estimated and their asymptotic properties are obtained.
Abstract: In this paper we present a stationary bivariate minification process with Marshall and Olkin exponential distribution. The process is given by Xn = K min(Xni1;Yni1;·n1); Yn = K min(Xni1;Yni1;·n2); where f(·n1;·n2);n ‚ 1g is a sequence of independent and identically distributed random vectors, the random vectors (Xm;Ym) and (·n1;·n2) are independent for m 0, ‚2 > 0, ‚12 > 0, K > (‚1+‚2+‚12)=‚12. The innovation distribution, the joint distribution of random vectors (Xn;Yn) and (Xnij;Ynij), j > 0, the autocovariance and the autocorrelation matrix are obtained. The unknown parameters are estimated and their asymptotic properties are obtained.
TL;DR: In this paper, the main purpose of the present paper is to characterize the classes (arc : f and f0), where f and F denote the spaces of almost convergent null sequences with real or complex terms.
Abstract: The sequence space arc have been defined and the classes (arc : lp) and (arc : c) of infinite matrices have been characterized by Aydin and Basar (On the new sequence spaces which include the spaces c0 and c, Hokkaido Math. J. 33(2) (2004), 383-398) [1], where 1 ≤ p ≤ ∞. The main purpose of the present paper is to characterize the classes (arc : f) and (arc : f0), where f and f0 denote the spaces of almost convergent and almost convergent null sequences with real or complex terms. .
TL;DR: In this paper, the authors prove existence and uniqueness results to three point boundary value problems associated with singular systems of first order differential equations by the use of generalized inverses of matrices.
Abstract: In this paper we prove existence and uniqueness results to three point boundary value problems associated with singular system of first order differential equations by the use of generalized inverses of matrices. .
TL;DR: In this paper, a unified class of functions of complex order is considered and necessary and sufficient conditions for these functions to be in this class are obtained, which generalizes the results obtained by Srivastava and Lashin [10] and Ravichandran et al. [4].
Abstract: In the present investigation, we consider an unified class of functions of complex order. Necessary and sufficient condition for functions to be in this class is obtained. The results obtained in this paper generalizes the results obtained by Srivastava and Lashin [10], and Ravichandran et al. [4]. .
TL;DR: In this article, a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space with P 1 n=1 r = 1 r is considered.
Abstract: Let K be a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T1;T2;:::;TN:K i! E be N asymptotically nonexpansive nonself mappings with sequences fr i ng such that P 1 n=1 r i
TL;DR: In this article, the notions of DS ⁄ -sets and DS � -continuous functions are introduced and their properties and their relationships with some other types of sets are investigated.
Abstract: In this paper, the notions of DS ⁄ -sets and DS ⁄ -continuous functions are introduced and their properties and their relationships with some other types of sets are investigated. Moreover, some new decompositions of continuous functions are obtained by using DS ⁄ -continuous functions, DS-continuous functions and D-continuous functions.
TL;DR: In this article, almost-convergence of double sequences (subsequences) is equivalent to almost Cauchy condition, and the set of all almost convergent subsequences of a sequence S = Snm is of the second category.
Abstract: Almost-convergence of double sequences (subsequences) is equivalent to almost Cauchy condition. If the set of all almost convergent subsequences of a sequence S = Snm is of the second category, then S is convergent in the simple sense. For the sequence S = Snm which almost converges to L, Lebesgue measure of the set of all its subsequences which almost converge to L is either 1 or 0. .
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TL;DR: In this article, some properties of GO-compact spaces and properties of g-continuous multifunctions are investigated in the context of multifunctions, and the authors also investigate properties of continuous GO compact spaces.
Abstract: The purpose of this paper is to oer some more properties of GO-compact spaces and to introduce and investigate some properties of g-continuous multifunctions. We also investigate GO-compact spaces in the context of multifunctions.
TL;DR: In this article, a new subclass of p-valent harmonic functions that are orientation preserving in the open unit disk and are related to Goodman-type analytic uniformly star like functions are introduced.
Abstract: In this paper, we have introduced a new subclass of p-valent harmonic functions that are orientation preserving in the open unit disk and are related to Goodman-type analytic uniformly star like functions. Coefficient bounds, distortion bounds, extreme points, convolution conditions and convex combination for the functions belonging to this class are obtained.
TL;DR: In this article, it was shown that if T has Property (F), then it is possible to prove that T ∩ GL(A) = Fred0T (A) iff ltsr (J) = 1.
Abstract: Let A and B be unital Banach algebras and T : A → B be a unital continuous homomorphism. Put J = Ker T. Let FredT (A) = {x e A|T (x) is invertible in B} and Fred0T(A) = {x + k|x is invertible in A, k e J}. In this note, we prove that if T has Property (F), then FredT (A) ∩ GL(A) = Fred0T (A) iff ltsr (J) = 1. .
TL;DR: In this paper, a common fixed point theorem for two pairs of weakly compatible mappings satisfying Altman type contraction in metric space is proved, which extends and improves several known results.
Abstract: In this paper, a common fixed point theorem for two pairs of weakly compatible mappings satisfying Altman type contraction in metric space is proved. Our result extends and improves several known results.
TL;DR: As a generalization of β-continuous functions, the authors introduced and studied several properties of weakly β continuous functions in bitopological spaces and obtained its several characterizations.
Abstract: As a generalization of β-continuous functions, we introduce and study several properties of weakly β-continuous functions in bitopological spaces and we obtain its several characterizations .
TL;DR: In this article, the integral representation of infinite sums involving the ratio of multiple binomial coecients is investigated and some well-known properties of the Zeta function are recovered.
Abstract: We investigate the integral representation of infinite sums involving the ratio of multiple binomial coecients. We also recover some well-known properties of the Zeta function.
TL;DR: In this article, Anderson et al. proved the inequalities for the volume of the unit ball in Rn for all n ≥ 1 and p ≥ 1, where VB denotes the volumes of Bーテ.
Abstract: Let B = {x Rn|||x||p ≤ 1} be the unit ball in l. We prove the inequalities for the volume of the B: V < V 2Γ(+1)VBV B for all n ≥ 1 and p ≥ 1, where VB denotes the volumes of B. Furthermore, we obtain the upper and lower bounds of V/ VB and VB/ VB. Our results are generalizations for inequalities in Rn proved and refined by G.D. Anderson et al., K.H. Borgwardt, D.A.Klain and G.-C. Rota and H. Alzer.
TL;DR: In this article, the explicit expressions of mixed and componentwise condition numbers for the hyperbolic QR factorization are derived, and the normwise and component-wise perturbation bounds are presented.
Abstract: We present normwise and componentwise perturbation bounds for the hyperbolic QR factorization by using a new approach. The explicit expressions of mixed and componentwise condition numbers for the hyperbolic QR factorization are derived.
TL;DR: In this article, the class of star-like multivalent meromorphic functions in a punctured disk with a simple pole of order p at the center of the disk is defined.
Abstract: Let T(p) be the class of multivalent meromorphic functions f(z) in a punctured disk Ų with a simple pole of order p at the center of disk is defined. We considered the class of star like multivalent meromorphic and convex multivalent meromorphic functions S(p);C(p), respectively. The coefficient properties are obtained and the star likeness and convexity of functions in T(p) are also investigated with some other results.
TL;DR: In this paper, the Sobolev inner product (f,g) was introduced and a Cohen type inequality for Fourier expansion in terms of the polynomials associated to the inner product was proved.
Abstract: Let introduce the Sobolev-type inner product (f,g)= where N≥0: In this paper we prove a Cohen type inequality for Fourier expansion in terms of the polynomials associated to the Sobolev inner product.