In this paper existence and uniqueness of fixed points are proved for self maps, satisfying a new contraction without assuming the compatibility commutative property maps. Some remarks applications to integral type given illustrate importance our results. An open problem future research is also given.

In this article, we introduce the concept of weak F?m,?-contractions on relation-theoretic m-metric spaces and establish related fixed point theorems, where ? is a control function ? relation. Then, detail some results for cyclic-type F?m,?-contraction mappings. Finally, demonstrate illustrative examples discuss upper lower solutions Volterra-type integral equations form ??=?0?A?,?,??m?+??,??0,1.

‎In this paper, based on [A. Razani, V. Rako$check{c}$evi$acute{c}$ and Z. Goodarzi, Nonself mappings in modular spaces and common fixed point theorems, Cent. Eur. J. Math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $T$ in the modular space $X_rho$ is presented. Moreover, we study a new version of Krasnoseleskii's fixed point theorem for $S+T$, where $T$ is a cont...

Abstract The objective of the present research is to establish and prove some new common fuzzy fixed-point theorems for set-valued mappings involving Θ-contractions in a complete metric space. For this purpose, novel integral-type contraction condition applied obtain these results. In way, several useful classical results have been generalized. Moreover, concrete example created furnish our An ...

We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...

Fractional calculus is the field of mathematical analysis which deals with the investigation and applications of integrals and derivatives of arbitrary order. The purpose of this work is to use Hadamard fractional integral to establish some new integral inequalities of Gruss type by using one or two parameters which ensues four main results . Furthermore, other integral inequalities of reverse ...

this paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. the boundary conditionsinvolved riemann-liouville fractional order derivative and integral. further, the non-linear function $f$ containfractional order derivative which produce extra complexity. thank to...

‎We study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎These equations will be converted to a system of‎ ‎singular integral equations with Cauchy type kernels‎. ‎Using‎ ‎Chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of Cauchy type singular integral equation which will ...