Recently Samet, Vetro and Vetro introduced the notion of α-ψ-contractive type mappings and established some fixed point theorems in complete metric spaces. In this paper, we introduce the notion of -contractive multifunctions and give a fixed point result for these multifunctions. We also obtain a fixed point result for self-maps in complete metric spaces satisfying a contractive condition.

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On fixed points of α-ψ-contractive multifunctions

In this paper, we extend the coupled fixed point theorems for mixed monotone operators F : X × X → X obtained by Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379–1393] and Luong and Thuan [N.V. Luong and N.X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011) 983–992], by weakening the involved contractive condition. An example as well as an application to nonlinear Fredholm integral equations is also given in order to illustrate the effectiveness of our generalizations.

Coupled fixed point theorems for ϕ-contractive mixed monotone mappings in partially ordered metric spaces

Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces

In this article the concept of coupled best proximity point and cyclic contraction pair are introduced and then we study the existence and convergence of these points in metric spaces. We also establish new results on the existence and convergence in a uniformly convex Banach spaces. Furthermore, we give new results of coupled fixed points in metric spaces and give some illustrative examples. An open problems are also given at the end for further investigation.

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Coupled best proximity point theorem in metric Spaces

In this article, we present tripled coincidence point theorems for F: X3 → X and g: X → X satisfying weak φ-contractions in partially ordered metric spaces. We also provide nontrivial examples to illustrate our results and new concepts presented herein. Our results unify, generalize and complement various known comparable results from the current literature, Berinde and Borcut and Abbas et al.

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Tripled coincidence point theorems for weak φ-contractions in partially ordered metric spaces

In this paper, we introduce the concept of tripled fixed point for nonlinear mappings in partially ordered complete metric spaces and obtain existence, and existence and uniqueness theorems for contractive type mappings. Our results generalize and extend recent coupled fixed point theorems established by Gnana Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379–1393]. Examples to support our new results are given.

Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces

We present new results on the existence and uniqueness of tripled fixed points for nonlinear mappings in partially ordered complete metric spaces that extend the results in the previous works: Berinde and Borcut, 2011, Borcut and Berinde, 2012, and Borcut, 2012. An example and an application to support our new results are also included in the paper.

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Tripled Fixed Point Theorems for Mixed Monotone Kannan Type Contractive Mappings

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Marin Borcut

Papers

Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces

Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces

Tripled Fixed Point Theorems for Mixed Monotone Kannan Type Contractive Mappings

Triple fixed point theorems for mixed monotone Presic-Kannan and Presic-Chatterjea mappings in partially ordered metric spaces