Scrutiny of some fixed point results by S-operators without triangular inequality
-
Farshid Khojasteh
und
Hassan Khandani
Abstract
In this work, the discussion centers on introducing non-triangular metric as a generalization of JS-metric, which may lessen the frantic pace of working on generalizing the triangle inequality by omitting it from the original ordinary metric’s definition. Then, we present S-operators as a new sort of mappings included some properties in order to characterize some known contractions. After that, we graft non-triangular metric onto S-operators in order to make the worthwhile fixed point results facile to prove and conceive.
The first author wishes to thank all the members of the Young Researcher and Elite Club of Islamic Azad University of Arak for completely supported the research cause of wining the Best Scholar Award in Markazi province in Iran at 2019.
Acknowledgement
The first author wishes to thank all the members of the Young Researcher and Elite Club of Islamic Azad University of Arak for completely supported the research cause of wining the Best Scholar Awards in Markazi province in Iran at 2019.
References
[1] Abbas, S.: Existence of solutions to fractional order ordinary and delay differential equations and applications, Electron. J. Diff. Equ. 9 (2011), 1–11.Suche in Google Scholar
[2] Banach, S.: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133–181.10.4064/fm-3-1-133-181Suche in Google Scholar
[3] Ćirić, L.: On contraction type mappings, Math. Balkanica 1 (1971), 52–57.Suche in Google Scholar
[4] Demma, M.—Saadati, R.—Vetro, P.: Fixed point results on b-metric space via Picard sequences and b-simulation functions, Iranian J. Math. Sci. Informat. 11(1) (2016), 123–136.10.1155/2015/189861Suche in Google Scholar
[5] Diethelm, K.: The Analysis of Fractional Differential Equation, Springer-Verlag, New York, 2010.10.1007/978-3-642-14574-2Suche in Google Scholar
[6] Hussain, N.—Kadelburg, Z.—Radenovic, S.—Al-Solamy, F.: Comparison functions and fixed point results in partial metric spaces, Abstr. Appl. Anal. (2012); http://dx.doi.org/10.1155/2012/605781.10.1155/2012/605781Suche in Google Scholar
[7] Hussain, N.—Kutbi, M. A.—Khaleghizadeh, S.—Salimi, P.: Discussions on recent results forα-ψ-contractive mappings, Abstr. Appl. Anal. (2014); http://dx.doi.org/10.1155/2014/456482.10.1155/2014/456482Suche in Google Scholar
[8] Jleli, M.—Samet, B.: A generalized metric space and related fixed point theorems, Fixed Point Theory Appl. (2015); https://doi.org/10.1186/s13663-015-0312-7.10.1186/s13663-015-0312-7Suche in Google Scholar
[9] Khandani, H.: A characterization for Meir-Keeler contractions, Rend. Circ. Mat. Palermo, II. Ser. 67(2) (2017), 251–265.10.1007/s12215-017-0312-zSuche in Google Scholar
[10] Khojasteh, F.—Shukla, S.—Radenović, S.: A new approach to the study of fixed point theorems via simulation functions, Filomat 29(6) (2015), 1189–1194.10.2298/FIL1506189KSuche in Google Scholar
[11] Khojasteh, F.—Razani, A.—Moradi, S.: A fixed point of generalizedTF-contraction mappings in cone metric spaces, Fixed Point Theory Appl. (2011); https://doi.org/10.1186/1687-1812-2011-14.10.1186/1687-1812-2011-14Suche in Google Scholar
[12] Khojasteh, F.—Du, W.-Sh.: New results and generalizations for approximate fixed point property and their applications, Abstr. Appl. Anal. (2014); https://doi.org/10.1155/2014/581267.10.1155/2014/581267Suche in Google Scholar
[13] Khojasteh, F.—Du, W.-Sh.—Chiu, Y. N.: Some generalizations of Mizoguchi-Takahashi’s fixed point theorem with new local constraints, Fixed Point Theory Appl. (2014); https://doi.org/10.1186/1687-1812-2014-31.10.1186/1687-1812-2014-31Suche in Google Scholar
[14] Kilbas, A. A.—Srivastava, H. M.—Trujillo, J. J.: Theory and Applications of Fractional Differential Equations, Elsevier Science Limited, 2006.Suche in Google Scholar
[15] Lakshmikantham, V.—Vatsala, A. S.: Basic theory of fractional differential equations, Nonlinear Anal. (TMA) 69(8) (2008), 2677–2682.10.1016/j.na.2007.08.042Suche in Google Scholar
[16] Mainardi, F.: Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics in Fractals and Fractional Calculus in Continuum Mechanics, Springer-Verlag, New York, 1997.10.1007/978-3-7091-2664-6Suche in Google Scholar
[17] Mizoguchi, N.—Takahashi, W.: Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989), 177–188.10.1016/0022-247X(89)90214-XSuche in Google Scholar
[18] Rhoades, B. E.: A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 224 (1977), 257–290.10.1090/S0002-9947-1977-0433430-4Suche in Google Scholar
[19] Rhoades, B. E.: Some theorems on weakly contractive maps, Nonlinear Anal. (TMA). 47 (2001), 2683–2693.10.1016/S0362-546X(01)00388-1Suche in Google Scholar
[20] Soleimani-Rad, G.—Radenović, S.—Dolićanin-Dekic, D.: A shorter and simple approach to study fixed point results via b-simulation functions, Iranian J. Math. Sci. Informat. 13(1) (2018), 97–102.Suche in Google Scholar
© 2020 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Regular papers
- Relatively residuated lattices and posets
- Strongly s-dense injective hull and Banaschewski’s theorems for acts
- Wild sets in global function fields
- Generators and integral points on elliptic curves associated with simplest quartic fields
- New Filbert and Lilbert matrices with asymmetric entries
- Returning functions with closed graph are continuous
- On sets of points of approximate continuity and ϱ-upper continuity
- Investigation of the fifth Hankel determinant for a family of functions with bounded turnings
- On solvability of some nonlocal boundary value problems for biharmonic equation
- The study of piecewise pseudo almost periodic solutions for impulsive Lasota-Wazewska model with discontinuous coefficients
- Strongly increasing solutions of higher-order quasilinear ordinary differential equations
- Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments
- Filippov solutions of vector Dirichlet problems
- Sequences of positive homoclinic solutions to difference equations with variable exponent
- Modified Lupaş-Jain operators
- New fixed point results in bv(s)-metric spaces
- Improved Young and Heinz operator inequalities for unitarily invariant norms
- Scrutiny of some fixed point results by S-operators without triangular inequality
- The lattices of families of regular sets in topological spaces
- Iterated partial summations applied to finite-support discrete distributions
- Hamiltonicity of a class of toroidal graphs
Artikel in diesem Heft
- Regular papers
- Relatively residuated lattices and posets
- Strongly s-dense injective hull and Banaschewski’s theorems for acts
- Wild sets in global function fields
- Generators and integral points on elliptic curves associated with simplest quartic fields
- New Filbert and Lilbert matrices with asymmetric entries
- Returning functions with closed graph are continuous
- On sets of points of approximate continuity and ϱ-upper continuity
- Investigation of the fifth Hankel determinant for a family of functions with bounded turnings
- On solvability of some nonlocal boundary value problems for biharmonic equation
- The study of piecewise pseudo almost periodic solutions for impulsive Lasota-Wazewska model with discontinuous coefficients
- Strongly increasing solutions of higher-order quasilinear ordinary differential equations
- Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments
- Filippov solutions of vector Dirichlet problems
- Sequences of positive homoclinic solutions to difference equations with variable exponent
- Modified Lupaş-Jain operators
- New fixed point results in bv(s)-metric spaces
- Improved Young and Heinz operator inequalities for unitarily invariant norms
- Scrutiny of some fixed point results by S-operators without triangular inequality
- The lattices of families of regular sets in topological spaces
- Iterated partial summations applied to finite-support discrete distributions
- Hamiltonicity of a class of toroidal graphs
