Abstract In this work we define the concepts of coupled orbit and orbitally completeness. After then, using method Bollenbacher Hicks [8], prove some Caristi type fixed point theorems in complete metric spaces for a function P : E × → E. We also give two examples that support our results.

*Correspondence: [email protected] 1Young Researcher and Elite Club, Arak-Branch, Islamic Azad University, Arak, Iran Full list of author information is available at the end of the article Abstract In this work, partial answers to Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s conjectures are presented via a light version of Caristi’s fixed point theorem. Moreover, we introduce th...

In this article, the existence and uniqueness of a fixed point were investigated using concept σ , γ -contractive in context Hausdorff metric space. A well-known Caristi type is primarily generalized by new results. The result improve...

In this paper, we present a new extension of Banach-Caristi type theorem for multivalued mappings. We show that our result is not consequence version Banach contraction principle due to Nadler. provide an application the solution functional equations.

Abstract In this paper we introduce some new types of contractive mappings by combining Caristi contraction, ?iri?-quasi contraction and weak in the framework a metric space. We prove fixed point theorems for such type over complete spaces with help ? -diminishing property. Some examples are given strengthening hypothesis our established theorems.

In this paper, we establish the existence of common coupled fixed point results for new Caristi type contraction of three covariant mappings in Bipolar metric spaces. Some interesting consequences of our results are achieved. Moreover, we give an illustration which presents the applicability of the achieved results.

* Correspondence: [email protected] Department of Mathematics, Faculty of Science For Girls, King Abdulaziz University, P.O. Box 53909, Jeddah 21593, Saudi Arabia Full list of author information is available at the end of the article Abstract Using the concept of u-distance, we prove a fixed point theorem for multivalued contractive maps. We also establish a multivalued version of the Caris...

In this paper a new class of mappings, known as locally λ-strongly φ-accretive mappings, where λ and φ have special meanings, is introduced. This class of mappings constitutes a generalization of the well-known monotone mappings, accretive mappings and strongly φ-accretive mappings. Subsequently, the above notion is used to extend the results of Park and Park, Browder and Ray to locally λ-stron...