A generalized Suzuki–Berinde contraction that characterizes Banach spaces
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Mujahid Abbas
Abstract
We introduce a large class of contractive mappings, called Suzuki–Berinde type contraction. We show that any Suzuki–Berinde type contraction has a fixed point and characterizes the completeness of the underlying normed space. A fixed point theorem for multivalued mappings is also obtained. These results unify, generalize and complement various known comparable results in the literature.
References
[1] S. Banach, Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales, Fund. Math. 3 (1922), 133–181. 10.4064/fm-3-1-133-181Search in Google Scholar
[2] I. Beg and S. M. A. Aleomraninejad, Fixed points of Suzuki type multifunctions on metric spaces, Rend. Circ. Mat. Palermo (2) 64 (2015), 203–207. 10.1007/s12215-015-0190-1Search in Google Scholar
[3] M. Edelstein, On fixed and periodic points under contractive mappings, J. Lond. Math. Soc. 37 (1962), 74–79. 10.1112/jlms/s1-37.1.74Search in Google Scholar
[4] M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal. 69 (2008), no. 9, 2942–2949. 10.1016/j.na.2007.08.064Search in Google Scholar
[5] T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861–1869. 10.1090/S0002-9939-07-09055-7Search in Google Scholar
[6] T. Suzuki, A new type of fixed point theorem in metric space, Nonlinear Anal. 71 (2009), 5313–5317. 10.1016/j.na.2009.04.017Search in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Around the Świątkowski-type conditions
- Metamorphism—an integral transform reducing the order of a differential equation
- Linear isomorphic spaces of Cesàro–Nörlund operator, their duals and matrix transformations
- A generalized Suzuki–Berinde contraction that characterizes Banach spaces
- Asymptotic behavior of solutions toward the constant state to the Cauchy problem for the non-viscous diffusive dispersive conservation law
- Trigonometric Hermite interpolation method for Fredholm linear integral equations
- Smoothing Levenberg–Marquardt algorithm for solving non-Lipschitz absolute value equations
- Two-dimensional EMD with shape-preserving spline interpolation
- Computing subdifferential limits of operators on Banach spaces
- Certain aspects of ℐ-statistical supremum and ℐ-statistical infimum of real-valued sequences
- Weighted Simpson-like type inequalities for quasi-convex functions
- Bochner formula in generalized (k,μ)-space forms
- Convergence of a conjugate function in Zygmund space by almost Nörlund transform
- 2-point left Radau-type inequalities via s-convexity
- A general size-biased distribution
- A study of fuzzy anti-λ-ideal convergent triple sequence spaces
- Euler-type integrals for the generalized hypergeometric matrix function
- Korn’s inequality in anisotropic Sobolev spaces
Articles in the same Issue
- Frontmatter
- Around the Świątkowski-type conditions
- Metamorphism—an integral transform reducing the order of a differential equation
- Linear isomorphic spaces of Cesàro–Nörlund operator, their duals and matrix transformations
- A generalized Suzuki–Berinde contraction that characterizes Banach spaces
- Asymptotic behavior of solutions toward the constant state to the Cauchy problem for the non-viscous diffusive dispersive conservation law
- Trigonometric Hermite interpolation method for Fredholm linear integral equations
- Smoothing Levenberg–Marquardt algorithm for solving non-Lipschitz absolute value equations
- Two-dimensional EMD with shape-preserving spline interpolation
- Computing subdifferential limits of operators on Banach spaces
- Certain aspects of ℐ-statistical supremum and ℐ-statistical infimum of real-valued sequences
- Weighted Simpson-like type inequalities for quasi-convex functions
- Bochner formula in generalized (k,μ)-space forms
- Convergence of a conjugate function in Zygmund space by almost Nörlund transform
- 2-point left Radau-type inequalities via s-convexity
- A general size-biased distribution
- A study of fuzzy anti-λ-ideal convergent triple sequence spaces
- Euler-type integrals for the generalized hypergeometric matrix function
- Korn’s inequality in anisotropic Sobolev spaces
