Generalized Meir-Keeler type contractions and discontinuity at fixed point II
-
Abhijit Pant
,
R. P. Pant
Abstract
This paper is a continuation of [Bisht, R. K.—Rakočević, V.: Generalized Meir-Keeler type contractions and discontinuity at fixed point, Fixed Point Theory 19(1) (2018), 57–64]. We obtain some fixed point theorems under contractive conditions which admit discontinuity at the fixed point. Our results subsume all the known results of similar type, provide new answers to the question of continuity of contractive mappings at their fixed points, and also rectify some recent results by Bisht and Rakočević. Many examples are given to illustrate our results.
The first author is thankful to Professor M. C. Josh for his valuable suggestions. The third author was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, Grant No. 174025.
Communicated by Gregor Dolinar
Acknowledgement
The authors thank the referee for his valuable suggestions for improving the presentation.
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© 2019 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Regular papers
- RNDr. Kvetoslava Dvořáková passed away
- On the Riesz structures of a lattice ordered abelian group
- On Diophantine equation x4 + y4 = n(u4 + v4)
- On a Waring-Goldbach problem involving squares and cubes
- D(n)-quadruples in the ring of integers of ℚ(√2, √3)
- Geometry of ℙ2 blown up at seven points
- Preservation of Rees exact sequences
- Pointwise multipliers between weighted copson and cesàro function spaces
- Some properties associated to a certain class of starlike functions
- Asymptotic properties of noncanonical third order differential equations
- Existence and regularity results for unilateral problems with degenerate coercivity
- Direct and inverse approximation theorems of functions in the Orlicz type spaces 𝓢M
- Some approximation properties of a kind of (p, q)-Phillips operators
- Best proximity points for a new type of set-valued mappings
- Weakly demicompact linear operators and axiomatic measures of weak noncompactness
- Fixed point results for F𝓡-generalized contractive mappings in partial metric spaces
- Einstein-Weyl structures on trans-Sasakian manifolds
- Characterizations of linear Weingarten space-like hypersurface in a locally symmetric Lorentz space
- ∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds
- Uncorrelatedness sets of discrete random variables via Vandermonde-type determinants
- A note on the consistency of wavelet estimators in nonparametric regression model under widely orthant dependent random errors
- On adaptivity of wavelet thresholding estimators with negatively super-additive dependent noise
- Generalized Meir-Keeler type contractions and discontinuity at fixed point II
