Mehmet Kir

New fixed point results in rectangular metric space and application to fractional calculus

Abstract In this paper, we introduce α-ψ type contractive mapping in rectangular metric space satisfying certain admissibility conditions and prove a fixed point result for such mapping in complete and Hausdorff rectangular metric space. Some examples are given to justify our result. Also we have shown that the existence of solution of a nonlinear fractional differential equation can be guaranteed, as an application of our result.

Coupled fixed point theorems in complete metric spaces endowed with a directed graph and application

Abstract The purpose of this paper is to present some existence results for coupled fixed point of a (φ,ψ) —contractive condition for mixed monotone operators in metric spaces endowed with a directed graph. Our results generalize the results obtained by Jain et al. in (International Journal of Analysis, Volume 2014, Article ID 586096, 9 pages). Moreover, we have an application to some integral system to support the results.

Some extensions for generalized (ϕ,ψ)-almost contractions

In this paper, we derive a new fixed point results in partially ordered b-metric-like spaces. Our results generalize and extend several well-known comparable results in the literature. Further, two examples are also given to show that our results are influential. c ©2016 All rights reserved.

On Contraction Mappings and Fixed Point Theorems in 2-Normed Spaces

In this paper, we introduce j contraction mappings in 2-normed spaces and we show that the mappings have a unique fixed point in 2-Banach spaces. Also, we introduced a new fixed point theorem for nonselfmappings applying the definition of retraction to 2-Banach spaces.