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...

This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: { D t x(t) = f(t, x(t), D β t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = ∫ 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle. Keywords—Fractional differential equation; Integral boundary condi...

‎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 In this article, we prove some novel fixed-point results for a pair of multivalued dominated mappings obeying new generalized Nashine–Wardowski–Feng–Liu-type contraction orbitally lower semi-continuous functions in complete orbital b -metric space. Furthermore, theorems are established the scenario ordered spaces. Some examples offered to demonstrate validity our results’ premise. To a...

In the paper by Khojasteh et al. 2010 , the authors tried to generalize Branciari’s theorem, introducing the new integral type contraction mappings. In this note we give a counterexample on their main statement Theorem 2.9 . Also we give a comment explaining what the mistake in the proof is, and suggesting what conditions might be appropriate in generalizing fixed point results to cone spaces, ...

In this paper, the notion of θ*-weak contraction is introduced, which utilized to prove some fixed point results. These results are helpful give a positive response certain open question raised by Kannan and Rhoades on existence contractive definition does not force mapping be continuous at point. Some illustrative examples also given support our As applications result, we investigate uniquenes...

Abstract: In this paper, we investigate the existence, uniqueness and multiplicity of positive solutions for nonlocal boundary value problems of fractional differential equation. Firstly, we reduce the problem considered to the equivalent integral equation. Secondly, the existence and uniqueness of positive solution is obtained by the use of contraction map principle and some Lipschitz-type con...

In this paper, we consider a class of boundary value problems of fractional differential equations with integral and anti-periodic boundary conditions, which is a new type of mixed boundary condition. By using the contraction mapping principle, Krasnosel’skii fixed point theorem, and Leray-Schauder degree theory, we obtain some results of existence and uniqueness. Finally, several examples are ...

‎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 ...

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 ...