Fixed point theorems of LW-type Lipschitz cyclic mappings in complete B-metric-like spaces

Document Type: Research Paper

Authors

1 Department of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610000, China.

2 Department of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610000, China

Abstract

The research of Fixed Point Theorems (FPTs) plays an important role in nonlinear analysis. It is of great theoretical significance and profound application value to study general abstract theory in a B-Metric-Like Space (BMLS). So, it is an important topic to study the Fixed Point Theory (FPT) in a BMLS. In this paper, for the purpose of introducing some new FPTs, a -type Lipschitz Cyclic Mapping (LTLCM) is first proposed by us in a complete BMLS, and we proved the existence theorem of fixed points of -type Lipschitz Cyclic Mappings (LTLCMs) in complete BLMS. Next, we also construct an example in a discrete complete BMLS to show and illustrate the effectiveness of . In the end, on the basis of the example, we show the calculation of the range of the parameter s that appears in B-Metric-Like Spaces (BMLSs). Our main theorems extend and develop existing results in the recent literature.

Keywords

Main Subjects


[1]      Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta mathematicae3(1), 133-181.

[2]      Kirk, W. A., Srinivasan, P. S., & Veeramani, P. (2003). Fixed points for mappings satisfying cyclical contractive conditions. Fixed point theory4(1), 79-89.

[3]      Matthews, S. G. (1994). Partial metric topology. Annals of the New York academy of sciences728(1), 183-197.

[4]      Hitzler, P., & Seda, A. K. (2000). Dislocated topologies. Journal of electrical engineering51(12), 3-7.

[5]      Zeyada, F. M., Hassan, G. H., & Ahmed, M. A. (2006). A generalization of a fixed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces. Arabian journal for science and engineering31(1A), 111.

[6]      Bakhtin, I. A. (1989). The contraction mapping principle in quasimetric spaces. Functional analysis, Gos. Ped. Inst. Unianowsk30, 26-37.

[7]       Czerwik, S. (1993). Contraction mappings in $ b $-metric spaces. Acta mathematica et informatica universitatis ostraviensis1(1), 5-11.

[8]      Amini-Harandi, A. (2012). Metric-like spaces, partial metric spaces and fixed points. Fixed point theory and applications2012(1), 204.

[9]      Amini-Harandi, A. (2015). Fixed point theorems for monotone operators in partially ordered metric-like spaces and application to integral equations. Journal of nonlinear convex anaysisl.

[10]  Alghamdi, M. A., Hussain, N., & Salimi, P. (2013). Fixed point and coupled fixed point theorems on b-metric-like spaces. Journal of inequalities and applications, (1), 402.

[11]  Klin-eam, C., & Suanoom, C. (2015). Dislocated quasi-b-metric spaces and fixed point theorems for cyclic contractions. Fixed point theory and applications, (1), 74.

[12]  Van An, T., Van Dung, N., Kadelburg, Z., & Radenović, S. (2015). Various generalizations of metric spaces and fixed point theorems. Revista de la real academia de ciencias exactas, fisicas y naturales. serie A. Matematicas109(1), 175-198.

[13]  Aydi, H., & Felhi, A. (2016). Best proximity points for cyclic Kannan-Chatterjea-Ciric type contractions on metric-like spaces. Journal of nonlinear sciences and applications (JNSA)9(5), 2458-2466.

[14]  Wu, H., & Wu, D. (2016). Some fixed point theorems in complete dislocated quasi-b-metric space. Journal of mathematics research8(4), 68.

[15]  Alsulami, H. H., Gülyaz, S., Karapınar, E., & Erhan, İ. M. (2016). An Ulam stability result on quasi-b-metric-like spaces. Open Mathematics14(1), 1087-1103.

[16]  Fan, X. (2016). Fixed point theorems for cyclic mappings in quasi-partial b-metric spaces. Journal of nonlinear sciences and applications (JNSA)9(5), 2175-2189.

[17]  Zoto, K., Rhoades, B. E., & Radenović, S. (2017). Some generalizations for (α− ψ, ϕ) $(alpha-psi,phi) $-contractions in b-metric-like spaces and an application. Fixed point theory and applications,  (1), 26.

[18]  Nashine, H. K., & Kadelburg, Z. (2017). Existence of solutions of cantilever beam problem via (α-β-FG)-contractions in b-metric-like spaces. Filomat31(11), 3057-3074.

[19]  Aydi, H., & Czerwik, S. (2018). Fixed point theorems in generalized b-metric spaces. Modern discrete mathematics and analysis (pp. 1-9). Springer, Cham.

[20]  Afshari, H., Kalantari, S., & Aydi, H. (2018). Fixed point results for generalized α− ψ-Suzuki-contractions in quasi-b-metric-like spaces. Asian-European journal of mathematics11(01), 1850012.

[21]  Zoto, K., Radenović, S., & Ansari, A. H. (2018). On some fixed point results for (s, p, α)-contractive mappings in b-metric-like spaces and applications to integral equations. Open mathematics16(1), 235-249.

[22]  Aydi, H., Felhi, A., & Sahmim, S. (2016). On common fixed points for (α, ψ)-contractions and generalized cyclic contractions in b-metric-like spaces and consequences. Journal of nonlinear sciences and applications (JNSA), 9, 2492-2510.

[23]  Lei, M., & Wu, D. p. (2017). Fixed point theorems concerning new type cyclic maps in complete b-metric-like spaces. Journal of Chengdu university of information technology, 2, 82-85.