Fixed point theorems for monotone operators and applications to nonlinear elliptic problems

Gordji et al. (2012) gave a generalization of Geraghty's theorem. The aim of this paper is to study the necessary conditions for the existence of coincidence and common fixed point of four mappings satisfying ( , )-generalized contractive condition in the setup of partial ordered metric spaces. Some examples are given to validate the definitions and results presented herein. 0 in a complete metric space , the sequence +1 = =

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“…Our results extend, unify, and generalize the comparable results in [8,[17][18][19]. For some details also see [20,21].…”

Section: Introductionsupporting

confidence: 86%

Common Fixed Point of (ψ, β)-Generalized Contractive Mappings in Partially Ordered Metric Spaces

Abbas

Zulfaqar

Radenović

2014

Chinese Journal of Mathematics

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“…[1], [2], [3], [5], [8], [12], [16], [17], [19], [20], [30], [33], [34], [41]) in the recent years. Most recently, Alam et al [2] extended foregoing results to generalized ϕ-contractions.…”

Section: Theorem 12 (Nieto and Rodríguez-lópezmentioning

confidence: 99%

Monotone Generalized Contractions in Ordered Metric Spaces

Alam¹,

Imdad²

2016

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, we prove some existence and uniqueness results on coincidence points for g-monotone mappings satisfying linear as well as generalized nonlinear contractivity conditions in ordered metric spaces. Our results generalize and extend two classical and well known results due to Ran and Reurings (Proc. Amer. Math. Soc. 132 (2004), no. 5, 1435-1443) and Nieto and Rodríguez-López (Acta Math. Sin. 23 (2007), no. 12, 2205-2212) besides similar other ones. Finally, as an application of one of our newly proved results, we establish the existence and uniqueness of solution of a first order periodic boundary value problem.

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“…Corollary 22 (Wu and Liu [52], Sintunavarat and Kumam [55]). Corollary 20 remains true if we replace condition (iv) by the following condition:…”

Section: Multi-tupled Fixed Point Theoremsmentioning

confidence: 99%

Unified multi-tupled fixed point theorems involving mixed monotone property in ordered metric spaces

2016

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In this paper, we introduce a generalized notion of monotone property and prove some results regarding existence and uniqueness of multi-tupled fixed points for nonlinear contraction mappings satisfying monotone property in ordered complete metric spaces. Our results unify several classical and well known n-tupled (including coupled, tripled and quadruple ones) fixed point results existing in literature.

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Fixed point theorems for monotone operators and applications to nonlinear elliptic problems

Cited by 14 publications

References 28 publications

Common Fixed Point of (ψ, β)-Generalized Contractive Mappings in Partially Ordered Metric Spaces

Common Fixed Point of (ψ, β)-Generalized Contractive Mappings in Partially Ordered Metric Spaces

Monotone Generalized Contractions in Ordered Metric Spaces

Unified multi-tupled fixed point theorems involving mixed monotone property in ordered metric spaces

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