Some Results on Generalized Pata–Suzuki Type Contractive Mappings

In this work, we establish new fixed point theorems for generalized Pata–Suzuki type contraction via α -admissible mapping in metric spaces and to prove some fixed point results for such mappings. Moreover, we give an example to illustrate our main result. Consequently, the results presented in this paper generalize and improve the corresponding results of the literature.

Nonunique Coincidence Point Results via Admissible Mappings

This paper is aimed at presenting some coincidence point results using admissible mapping in the framework of the partial b -metric spaces. Observed results of the article cover a number of existing works on the topic of “investigation of nonunique fixed points.” We express an example to indicate the validity of the observed outcomes.

An extension of Karapinar and Sadaranganis’ result through the C-class functions by using α-admissible mapping with applications

The main objective of this work is to introduce a new type of non-linear contraction via C-class functions by using ?-admissible mapping. Our new results extend and generalize the very recent results of Karapinar and Sadarangani (2015. RACSAM. [37]). Illustrative examples are given to support our new findings. We have shown that our results satisfy the periodic fixed point results after modifying the contraction. Next, we extend our main findings from a self-mapping T to two self-mappings T; S. Also, an example is provided to justify the effectiveness of our new result on two self mappings, where the partially ordered structure fails. Finally, we apply our new findings to solve ordinary differential and non-linear integral equations.

Solving a nonlinear integral equation via orthogonal metric space

<abstract><p>We propose the concept of orthogonally triangular $ \alpha $-admissible mapping and demonstrate some fixed point theorems for self-mappings in orthogonal complete metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by our results. An instance to help our outcome is presented. We also explore applications of our key results.</p></abstract>

Unique Fixed-Point Results for β-Admissible Mapping under (β-ψˇ)-Contraction in Complete Dislocated Gd-Metric Space

This paper is designed to display some results which generalize the recent results that cannot be established from the corresponding results in other spaces and do not satisfy the remarks of Jleli et al. (Fixed Point Theor Appl. 210, 2012) and Samet et al. (Int. J. Anal. Article ID 917158, 2013). We obtain unique fixed-point for mapping satisfying β-ψˇ contraction only on a closed Gd ball in complete dislocated Gd-metric space. An example is also discussed to shed light on the main result.

Fractional Hybrid Differential Equations and Coupled Fixed-Point Results for α-Admissible Fψ1,ψ2−Contractions in M−Metric Spaces

In this paper, we investigate the existence of a unique coupled fixed point for α−admissible mapping which is of Fψ1,ψ2−contraction in the context of M−metric space. We have also shown that the results presented in this paper would extend many recent results appearing in the literature. Furthermore, we apply our results to develop sufficient conditions for the existence and uniqueness of a solution for a coupled system of fractional hybrid differential equations with linear perturbations of second type and with three-point boundary conditions.

On Wong Type Contractions

In this paper, by using admissible mapping, Wong type contraction mappings are extended and investigated in the framework of quasi-metric spaces to guarantee the existence of fixed points. We consider examples to illustrate the main results. We also demonstrate that the main results of the paper cover several existing results in the literature.

Coincidence Point Results for Multivalued Suzuki Type Mappings Using θ-Contraction in b-Metric Spaces

In this paper, we introduce the concept of coincidence best proximity point for multivalued Suzuki-type α -admissible mapping using θ -contraction in b-metric space. Some examples are presented here to understand the use of the main results and to support the results proved herein. The obtained results extend and generalize various existing results in literature.