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Some new results in Menger PbM-spaces for single-valued and multi-valued mappings via simulation functions with its application | ||
International Journal of Nonlinear Analysis and Applications | ||
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 05 آذر 1403 اصل مقاله (426.1 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.27258.3681 | ||
نویسندگان | ||
Ehsan Lotfali Ghasab؛ Reza Chaharpashlou* | ||
Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran | ||
تاریخ دریافت: 12 تیر 1401، تاریخ بازنگری: 29 شهریور 1401، تاریخ پذیرش: 05 مهر 1401 | ||
چکیده | ||
The main goal of the present paper is to obtain several fixed point theorems for both multi-valued and single-valued mappings in Menger $PbM$-spaces, which is an extension of Menger $PM$-spaces. In this paper, we introduce different types of contractive mappings by introducing the notions of $(\alpha-\psi)$-E-type simulation function and $(\beta-\psi)$-E-type simulation function in Menger $PbM$-spaces which is a generalization of simulation functions introduced by Khojasteh. Furthermore, we present some nontrivial examples and an application to the existence of a solution of the Volterra-type integral equation. | ||
کلیدواژهها | ||
Menger $PbM$-spaces؛ simulation function؛ self mappings؛ orbital admissible mappings؛ multi-valued mapping | ||
مراجع | ||
[1] R. Agarwal, U.P. Sharma, and R.P. Agarwal, Bicomplex Mittag-Leffler function and associated properties, J. Nonlinear Sci. Appl. 15 (2022), no. 1, 48–60. [2] H. Aydi, E. Karapinar, and V. Rakoccevic, Nonunique fixed point theorems on b-metric spaces via simulation function, Jordan J. Math. Statist. 12 (2019), no. 3, 265–288. [3] I.A. Bakhtin, The contraction mapping principle in almost metric space, Funct. Anal. 30 (1989), 26–37. [4] V. Berinde, Generalized contractions in quasi-metric spaces, Sem. Fixed Point Theory, Babes-Bolyai University, Research Sem., 1993, pp. 3–9. [5] T. Bhaskar and V. Lakshmikantham, Fixed point theory in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379–1393. [6] B.S. Choudhury and K.P. Das, A new contraction principle in Menger spaces, Acta Math. Sin. (Engl. Ser.) 24 (2008), 1379–1386. [7] R. Chaharpashlou and R. Saadati, Ulam–Hyers–Rassias stability for nonlinear ψ-Hilfer stochastic fractional differential equation with uncertainty, Adv. Differ. Equ. 2020 (2020), 339. [8] R. Chaharpashlou and R. Saadati, Best approximation of a nonlinear fractional Volterra integro-differential equation in matrix MB-space, Adv. Differ. Equ. 2021 (2021), 118. [9] R. Chaharpashlou, R. Saadati, D. O’Regan, and C. Park, C∗-algebra valued fuzzy normed spaces with application of Hyers–Ulam stability of a random integral equation, Adv. Differ. Equ. 2020 (2020), 326. [10] L. Ciric, Solving the Banach fixed point principle for nonlinear contractions in probabilistic metric spaces, Nonlinear Anal. 72 (2010), 2009–2018. [11] L. Ciri´c, D. Mihet, and R. Saadati, ´ Monotone generalized contractions in partially ordered probabilistic metric spaces, Topol. Appl. 156 (2009), 2838–2844. [12] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inf. Univ. Ostrav. 1 (1993), 5–11. [13] D. Gopal, M. Abbas, and C. Vetro, Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation, Appl. Math. Comput. 232 (2014), 955–967. [14] O. Hadzic and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic, Dordrecht, 2001. [15] O. Hadzic and E. Pap, Fixed point theorems for single-valued and multivalued mappings in probabilistic metric space, Atti Sem. Mat. Fiz. Modena 51 (2003), no. 2, 377–395. [16] F. Hasanvand and M. Khanehgir, Some fixed point theorems in Menger PbM-spaces with an application, Fixed Point Theory Appl. 2015 (2015), 81. [17] J. Jachymski, On probabilistic ϕ-contractions on Menger spaces, Nonlinear Anal. 73 (2010), 2199–2203. [18] F. Khojasteh, S. Shukla, and S. Radenovic, A new approach to the study of fixed point theorems via simulation functions, Filomat 29 (2015), no. 6, 1189–1194 [19] W. Kirk and N. Shahzad, Fixed Point Theory in Distance Spaces, Springer, Switzerland, 2014. [20] D. Mihet, Multivalued generalizations of probabilistic contractions, J. Math. Anal. Appl. 304 (2005), 464–472. [21] K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. USA. 28 (1942), 535–537. [22] X. Mu, C. Zhu, and Z. Wu, New multipled common fixed point theorems in Menger PM-spaces, Fixed Point Theory Appl. 2015 (2015), 136. [23] E.L. Ghasab, H. Majani, M. De la Sen, and G.S. Rad, e-Distance in Menger PGM spaces with an application, Axioms 10 (2021), no. 1, 3. [24] E.L. Ghasab, H. Majani, E. Karapinar, and G.S. Rad, New fixed point results in F-quasi-metric spaces and an application, Adv. Math. Phys. 2020 (2020), Article ID 9452350, 6 pages. [25] E.L. Ghasab, H. Majani, and G.S. Rad, Fixed points of set-valued F-contraction operators in quasi-ordered metric spaces with an application to integral equations, J. Siber. Fed. Univ. Math. Phys. 14 (2021), no. 2, 150–158. [26] P. Long, G. Murugusundaramoorthy, H. Tang, and W. Wang, Subclasses of analytic and bi-univalent functions involving a generalized Mittag-Leffler function based on quasi-subordination, J. Math. Comput. Sci. 26 (2022), no. 4, 379–394. [27] K. Owais, A. Serkan, and S. Mohd, Fractional calculus formulas for Mathieu-type series and generalized Mittag-Leffler function, J. Math. Comput. Sci. 20 (2020), no. 2, 122–130. [28] Z. Sadeghi and S.M. Vaezpour, Fixed point theorems for multivalued and single-valued contractive mappings on Menger PM spaces with applications, J. Fixed Point Theory Appl. 20 (2018), no. 3, 114. [29] H. Rahimi and G. Soleimani Rad, Fixed Point Theory in Various Spaces, Lambert Academic Publishing (LAP), Deutschland, Germany, 2013. [30] A. Rana Safdar, M. Shahid, and A. Muhammad Mumtaz, A class of fractional integral operators with multi-index Mittag-Leffler k-function and Bessel k-function of first kind, J. Math. Comput. Sci. 22 (2021), no. 3, 266–281. [31] I.A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001. [32] G. Soleimani Rad, S. Shukla, and H. Rahimi, Some relations between n-tuple fixed point and fixed point results, Rev. Real Acad. Cien. Exactas F´ıs. Natur. Ser. A. Mate. 109 (2015), 471–481. [33] B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland Series in Prob. & Appl. Math. (vol. 5), Amsterdam, 1983. [34] V.M. Sehgal and A.T. Bharucha-Reid, Fixed point of contraction mappings on PM-spaces, Math. Syst. Theory 6 (1972), 97–102. | ||
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