Fixed point results for decreasing convex orbital operators in Hilbert spaces

Petruşel, Adrian; Petruşel, Gabriela

doi:10.1007/s11784-021-00873-1

Cited by 5 publications

(5 citation statements)

References 15 publications

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“…Popescu [14] generalized the convex orbital β-Lipschitz mapping and considered the class of convex orbital (α, β)-Lipschitz mappings. He generalized and complemented the results in [13] for convex orbital (α, β)-Lipschitz mappings in Hilbert spaces.…”

Section: Introductionmentioning

confidence: 85%

“…for all ξ ∈ Y . Remark 3.2 It is shown in [13] that this class of mappings includes the following class of mappings:…”

Section: Convex Orbital (α β)-Contraction Mappingmentioning

confidence: 99%

“…Recently, Petruşel and Petruşel [13] considered the class of convex orbital β-Lipschitz mappings (see Definition 3.1) in the setting of Hilbert spaces. They showed that many important contraction mappings were properly contained in this class (see Remark 3.2).…”

Section: Introductionmentioning

confidence: 99%

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Some fixed-point theorems of convex orbital $(\alpha, \beta )$-contraction mappings in geodesic spaces

Shukla

2023

Fixed Point Theory Algorithms Sci Eng

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The aim of this paper is to broaden the applicability of convex orbital $(\alpha, \beta )$ ( α , β ) -contraction mappings to geodesic spaces. This class of mappings is a natural extension of iterated contraction mappings. The paper derives fixed-point theorems both with and without assuming continuity. Furthermore, the paper investigates monotone convex orbital $(\alpha, \beta )$ ( α , β ) -contraction mappings and establishes a fixed-point theorem for this class of mappings.

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Section: Introductionmentioning

confidence: 85%

“…for all ξ ∈ Y . Remark 3.2 It is shown in [13] that this class of mappings includes the following class of mappings:…”

Section: Convex Orbital (α β)-Contraction Mappingmentioning

confidence: 99%

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Some fixed-point theorems of convex orbital $(\alpha, \beta )$-contraction mappings in geodesic spaces

Shukla

2023

Fixed Point Theory Algorithms Sci Eng

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“…The reader can see more details on enrich nonexpansive mappings in [5]. • Can we mix the idea in this paper and fixed point results for decreasing convex orbital operators in Hilbert spaces in [16] to investigate some new development? • Can we use the sufficient condition of the equality of the fixed point of a double averaged mapping and its initial mapping to extend the results of other types of enriched mappings (see in [7,12])?…”

Section: Conclusion and Open Questionmentioning

confidence: 99%

On approximating fixed points of weak enriched contraction mappings via Kirk's iterative algorithm in Banach spaces

NITHIARAYAPHAKS¹,

SINTUNAVARAT²

2022

CJM

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Recently Berinde and Păcurar [Approximating fixed points of enriched contractions in Banach spaces. {\em J. Fixed Point Theory Appl.} {\bf 22} (2020), no. 2., 1--10], first introduced the idea of enriched contraction mappings and proved the existence of a fixed point of an enriched contraction mapping using the well-known fact that any fixed point of {the averaged mapping $T_\lambda$, where $\lambda\in (0,1]$, is also a fixed point of the initial mapping $T$}. In this work, we introduce the idea of weak enriched contraction mappings, and a new generalization of an averaged mapping called double averaged mapping. The first attempt is to prove the existence and uniqueness of the fixed point of a double averaged mapping associated with a weak enriched contraction mapping. Based on this result on Banach spaces, we give some sufficient conditions for the equality of all fixed points of a double averaged mapping and the set {of all fixed points of a weak enriched contraction mapping.} Moreover, our results show that an appropriate Kirk's iterative algorithm can be used to approximate a fixed point of a weak enriched contraction mapping. An illustrative example for showing the efficiency of our results is given.

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“…Recent research by Petruşel and Petruşel [14] and Popescu [15] has focused on convex orbital β-Lipschitz mappings and convex orbital (α, β)-Lipschitz mappings, respectively, in Hilbert spaces (see also [16]). They demonstrated the existence of fixed points within these classes of mappings and established connections with the admissible perturbations approach.…”

Section: Introductionmentioning

confidence: 99%

Convex (α, β)-Generalized Contraction and Its Applications in Matrix Equations

Shukla,

Sinkala

2023

Axioms

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This paper investigates the existence and convergence of solutions for linear and nonlinear matrix equations. This study explores the potential of convex (α,β)-generalized contraction mappings in geodesic spaces, ensuring the existence of solutions for both linear and nonlinear matrix equations. This paper extends the concept to partially ordered geodesic spaces and establishes new existence and convergence results. Illustrative examples are provided to demonstrate the practical relevance of the findings. Overall, this research contributes a novel approach to the field of matrix equations.

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Fixed point results for decreasing convex orbital operators in Hilbert spaces

Cited by 5 publications

References 15 publications

Some fixed-point theorems of convex orbital $(\alpha, \beta )$-contraction mappings in geodesic spaces

Some fixed-point theorems of convex orbital $(\alpha, \beta )$-contraction mappings in geodesic spaces

On approximating fixed points of weak enriched contraction mappings via Kirk's iterative algorithm in Banach spaces

Convex (α, β)-Generalized Contraction and Its Applications in Matrix Equations

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