Journal•ISSN: 1229-1595

# Nonlinear functional analysis and applications

About: Nonlinear functional analysis and applications is an academic journal. The journal publishes majorly in the area(s): Banach space & Fixed-point theorem. It has an ISSN identifier of 1229-1595. Over the lifetime, 345 publications have been published receiving 1068 citations.

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TL;DR: In this article, a contractive definition of fixed point theorems for mappings in fuzzy metric spaces is given, which does not require the mapping to be continuous at the fixed point.

Abstract: In this paper, we prove some general fixed point theorems, which generalize the result of Pant [4] for mappings in fuzzy metric spaces. Here we give the existence of a contractive definition which generates a fixed point, but does not force the mapping to be continuous at the fixed point.

60 citations

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TL;DR: In this paper, the basic results of oscillation theory of the Sturm-Liouville linear differential equation were extended to the half-linear dynamic equation, where the Riccati technique and variational principle were used.

Abstract: In this paper we show how the basic results of oscillation theory of the Sturm--Liouville linear differential equation $$ (r(t)y')'+p(t)y=0 $$ can be extended to the half-linear dynamic equation $$ (r(t)\Phi(y^\Delta))^\Delta+p(t)\Phi(y^\sigma)=0 \tag{HL$^\Delta$E} $$ on an arbitrary time scale, where $\Phi(x)=|x|^{\alpha-1}\sgn x$ with $\alpha>1$. In particular, the generalization of the so called Roundabout theorem is proved for equation (HL$^\triangle$E), which provides powerful tools for the investigation of oscillatory properties of this equation, namely the Riccati technique and variational principle. As an application we present Sturmian theory, oscillation and nonoscillation criteria for (HL$^\Delta$E). The questions concerning the existence and uniqueness of a solution of initial value problem are also discussed.

44 citations

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TL;DR: In this paper, a fixed point theorem of Schaefer type involving the product of two operators in a Banach algebra is proved and it is further applied to a first order nonlinear functional differential equation for proving an existence theorem under the mixed generalized Lipschitz and Caratheodory condition.

Abstract: In this paper a fixed point theorem of Schaefer type involving the product of two operators in a Banach algebra is proved and it is further applied to a first order nonlinear functional differential equation for proving an existence theorem under the mixed generalized Lipschitz and Caratheodory condition.

33 citations

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TL;DR: In this paper, Hadamard inequalities for k -fractional Riemann-Liouville integrals were deduced and extended to two-coordinate integrals.

Abstract: In this paper, we prove Hadamard inequalities for k -fractional Riemann-Liouville integrals and Hadamard inequalities for fractional Riemann-Liouville integrals are deduced. Also we extend these results on two coordinates and Hadamard inequalities for fractional Riemann-Liouville integrals on two coordinates are deduced.

30 citations

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TL;DR: In this article, a new summation-integral type sequence of linear positive operators Bn(f, x) was introduced, and the direct and inverse results in simultaneous approximation for these new sequences were studied.

Abstract: In the present paper, we introduce a new summation-integral type sequence of linear positive operators Bn(f, x). And study some direct and inverse results in simultaneous approximation for these new sequences.

30 citations