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On (α,φ)-weak Pata contractions

Year 2022, Volume: 10 Issue: 2, 228 - 240, 31.12.2022

Merve Aktay Murat Özdemir

https://doi.org/10.51354/mjen.1085695
Cited By: 1

Abstract

In this paper, we give (α,φ)-weak Pata contractive mapping by using the simulation function and multivalued (α,φ)-weak Pata contractions and establish some fixed point results for such contractions. Also, we give an example related to (α,φ)-weak Pata contractive mappings via simulation function. Our results generalize some Pata-type contractions and Banach contractions. Consequently, the obtained results encompass several results in the literature.

Keywords

fixed point pata contraction φ-weak contraction metric spaces

Thanks

The first author would like to thank TUBITAK (the Scientific and Technological Research Council of Turkey) for their financial support during her Ph.D. studies.

References

  • [1] Alber Ya.I., Guerre-Delabriere S., "Principle of weakly contractive maps in Hilbert spaces", in: I. Gohberg, Yu. Lyubich (Eds.), New Results in Theory Operator Theory, in Advances and Appl., Birkhauser, Basel 98, (1997), 7-22.
  • [2] Aktay M., Özdemir M., "Common fixed point results for a class of (α,β)-Geraghty contraction type mappings in modular metric spaces", Erzincan University Journal of Science and Technology, 13 (Special Issue-I), (2020), 150-161.
  • [3] Aktay M., Özdemir M., "Some results on generalized Pata--Suzuki type contractive mappings", Journal of Mathematics, (2021), Article ID 2975339, 9.
  • [4] Asl J.H., Rezapour S., Shahzad N, "On fixed points of α-ψ-contractive multifunctions", Fixed Point Theory Appl., (2012), 212.
  • [5] Argoubi H., Samet B., Vetro C., "Nonlinear contractions involving simulation functions in a metric space with a partial order", J. Nonlinear Sci. Appl., 8, (2015), 1082-1094.
  • [6] Balasubramanian S., "A Pata-type fixed point theorem", Math. Sci., 8, (2014), 65-69.
  • [7] Banach S., "Sur les opérationes dans les ensembles abstraits et leur application aux équation intégrales", Fundam. Math., 3, (1922), 133-181.
  • [8] Beg I., Azam A., "Fixed points of asymptotically regular multivalued mappings", J. Austral. Math. Soc. (Series-A), 53, (1992), 313-326.
  • [9] Chakraborty M., Samanta S.K., "On a fixed point theorem for a cyclical Kannan-type mapping", Facta Univ. Ser. Math. Inform., 28, (2013), 179-188.
  • [10] Eshaghi M., Mohsen S., Delavar M.R., De La Sen M., Kim G.H., Arian, A., "Pata contractions and coupled type fixed points", Fixed Point Theory Appl., 1, (2014), 130.
  • [11] Hong S.H., "Fixed points of multivalued operators in ordered metric spaces with applications", Nonlinear Anal., 72, (2009), 3929-3942.
  • [12] Kadelburg Z., Radenovic S., "Fixed point theorems under Pata-type conditions in metric spaces", J. Egypt. Math. Soc., 24, (2016), 77-82.
  • [13] Karapınar E., Kumam P., Salimi P., "On α-ψ-Meir-Keeler contractive mappings", Fixed Point Theory and Applications, 94, (2013).
  • [14] Karapınar E., "Fixed points results via simulation functions", Filomat, 30(8), (2016), 2343-2350.
  • [15] Khojasteh F., Shukla S., Radenovic S., "A new approach to the study of fixed point theorems via simulation functions", Filomat, 29(6), (2015), 1189-1194.
  • [16] Kolagar S.M., Ramezani M., Eshaghi M., "Pata type fixed point theorems of multivalued operators in ordered metric spaces with applications to hyperbolic differential inclusions", U.P.B. Sci. Bull., Series A, 78(4), (2016).
  • [17] Mohammadi B., Rezapour S., Shahzad N., "Some results on fixed points of α-ψ-Ciric generalized multifunctions", Fixed Point Theory Appl., (2013), 24.
  • [18] Nadler S.B., Multivalued contraction mappings, Pacific J Math., 30, (1969), 475-488.
  • [19] Nieto J.J., Rodriguez-Lope R., "Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations", Order, 72, (2005), 223-239.
  • [20] Paknazar M., Eshaghi M., Cho Y.J., Vaezpour S.M., "A Pata-type fixed point theorem in modular spaces with application", Fixed Point Theory Appl., (2013), 239.
  • [21] Pata V., "A fixed point theorem in metric spaces", J. Fixed Point Theory Appl., 10, (2011), 299-305.
  • [22] Patel D.P., "Fixed points of multivalued contractions via generalized class of simulation functions", Bol. Soc. Paran. Math., 38(3), (2020), 161-176. [23] Radenovic S., Kadelburg Z., Jandrlic D., Jandrlic A., "Some results on weakly contractive maps", Bull. Iranian Math. Soc., 38(3), (2012), 625.
  • [24] Rhoades B.H., "Some theorems on weakly contractive maps", Nonlinear Analysis, 47, (2001), 2683-2693.
  • [25] Samet B., Vetro C., Vetro P., "Fixed point theorem for (α,ψ)-contractive type mapping", Nonlinear Analysis, 75, (2012), 2154-2165.
  • [26] Zhang Q., Song Y., "Fixed point theory for generalized ϕ-weak contractions" Applied Mathematics Letters, 22, (2009), 75-78.

Year 2022, Volume: 10 Issue: 2, 228 - 240, 31.12.2022

Merve Aktay Murat Özdemir

https://doi.org/10.51354/mjen.1085695
Cited By: 1

Abstract

References

  • [1] Alber Ya.I., Guerre-Delabriere S., "Principle of weakly contractive maps in Hilbert spaces", in: I. Gohberg, Yu. Lyubich (Eds.), New Results in Theory Operator Theory, in Advances and Appl., Birkhauser, Basel 98, (1997), 7-22.
  • [2] Aktay M., Özdemir M., "Common fixed point results for a class of (α,β)-Geraghty contraction type mappings in modular metric spaces", Erzincan University Journal of Science and Technology, 13 (Special Issue-I), (2020), 150-161.
  • [3] Aktay M., Özdemir M., "Some results on generalized Pata--Suzuki type contractive mappings", Journal of Mathematics, (2021), Article ID 2975339, 9.
  • [4] Asl J.H., Rezapour S., Shahzad N, "On fixed points of α-ψ-contractive multifunctions", Fixed Point Theory Appl., (2012), 212.
  • [5] Argoubi H., Samet B., Vetro C., "Nonlinear contractions involving simulation functions in a metric space with a partial order", J. Nonlinear Sci. Appl., 8, (2015), 1082-1094.
  • [6] Balasubramanian S., "A Pata-type fixed point theorem", Math. Sci., 8, (2014), 65-69.
  • [7] Banach S., "Sur les opérationes dans les ensembles abstraits et leur application aux équation intégrales", Fundam. Math., 3, (1922), 133-181.
  • [8] Beg I., Azam A., "Fixed points of asymptotically regular multivalued mappings", J. Austral. Math. Soc. (Series-A), 53, (1992), 313-326.
  • [9] Chakraborty M., Samanta S.K., "On a fixed point theorem for a cyclical Kannan-type mapping", Facta Univ. Ser. Math. Inform., 28, (2013), 179-188.
  • [10] Eshaghi M., Mohsen S., Delavar M.R., De La Sen M., Kim G.H., Arian, A., "Pata contractions and coupled type fixed points", Fixed Point Theory Appl., 1, (2014), 130.
  • [11] Hong S.H., "Fixed points of multivalued operators in ordered metric spaces with applications", Nonlinear Anal., 72, (2009), 3929-3942.
  • [12] Kadelburg Z., Radenovic S., "Fixed point theorems under Pata-type conditions in metric spaces", J. Egypt. Math. Soc., 24, (2016), 77-82.
  • [13] Karapınar E., Kumam P., Salimi P., "On α-ψ-Meir-Keeler contractive mappings", Fixed Point Theory and Applications, 94, (2013).
  • [14] Karapınar E., "Fixed points results via simulation functions", Filomat, 30(8), (2016), 2343-2350.
  • [15] Khojasteh F., Shukla S., Radenovic S., "A new approach to the study of fixed point theorems via simulation functions", Filomat, 29(6), (2015), 1189-1194.
  • [16] Kolagar S.M., Ramezani M., Eshaghi M., "Pata type fixed point theorems of multivalued operators in ordered metric spaces with applications to hyperbolic differential inclusions", U.P.B. Sci. Bull., Series A, 78(4), (2016).
  • [17] Mohammadi B., Rezapour S., Shahzad N., "Some results on fixed points of α-ψ-Ciric generalized multifunctions", Fixed Point Theory Appl., (2013), 24.
  • [18] Nadler S.B., Multivalued contraction mappings, Pacific J Math., 30, (1969), 475-488.
  • [19] Nieto J.J., Rodriguez-Lope R., "Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations", Order, 72, (2005), 223-239.
  • [20] Paknazar M., Eshaghi M., Cho Y.J., Vaezpour S.M., "A Pata-type fixed point theorem in modular spaces with application", Fixed Point Theory Appl., (2013), 239.
  • [21] Pata V., "A fixed point theorem in metric spaces", J. Fixed Point Theory Appl., 10, (2011), 299-305.
  • [22] Patel D.P., "Fixed points of multivalued contractions via generalized class of simulation functions", Bol. Soc. Paran. Math., 38(3), (2020), 161-176. [23] Radenovic S., Kadelburg Z., Jandrlic D., Jandrlic A., "Some results on weakly contractive maps", Bull. Iranian Math. Soc., 38(3), (2012), 625.
  • [24] Rhoades B.H., "Some theorems on weakly contractive maps", Nonlinear Analysis, 47, (2001), 2683-2693.
  • [25] Samet B., Vetro C., Vetro P., "Fixed point theorem for (α,ψ)-contractive type mapping", Nonlinear Analysis, 75, (2012), 2154-2165.
  • [26] Zhang Q., Song Y., "Fixed point theory for generalized ϕ-weak contractions" Applied Mathematics Letters, 22, (2009), 75-78.
There are 25 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Merve Aktay 0000-0002-7213-4070

Murat Özdemir This is me 0000-0002-4928-3115

Early Pub Date December 31, 2022
Publication Date December 31, 2022
Published in Issue Year 2022 Volume: 10 Issue: 2

Cite

APA Aktay, M., & Özdemir, M. (2022). On (α,φ)-weak Pata contractions. MANAS Journal of Engineering, 10(2), 228-240. https://doi.org/10.51354/mjen.1085695
AMA Aktay M, Özdemir M. On (α,φ)-weak Pata contractions. MJEN. December 2022;10(2):228-240. doi:10.51354/mjen.1085695
Chicago Aktay, Merve, and Murat Özdemir. “On (α,φ)-Weak Pata Contractions”. MANAS Journal of Engineering 10, no. 2 (December 2022): 228-40. https://doi.org/10.51354/mjen.1085695.
EndNote Aktay M, Özdemir M (December 1, 2022) On (α,φ)-weak Pata contractions. MANAS Journal of Engineering 10 2 228–240.
IEEE M. Aktay and M. Özdemir, “On (α,φ)-weak Pata contractions”, MJEN, vol. 10, no. 2, pp. 228–240, 2022, doi: 10.51354/mjen.1085695.
ISNAD Aktay, Merve - Özdemir, Murat. “On (α,φ)-Weak Pata Contractions”. MANAS Journal of Engineering 10/2 (December 2022), 228-240. https://doi.org/10.51354/mjen.1085695.
JAMA Aktay M, Özdemir M. On (α,φ)-weak Pata contractions. MJEN. 2022;10:228–240.
MLA Aktay, Merve and Murat Özdemir. “On (α,φ)-Weak Pata Contractions”. MANAS Journal of Engineering, vol. 10, no. 2, 2022, pp. 228-40, doi:10.51354/mjen.1085695.
Vancouver Aktay M, Özdemir M. On (α,φ)-weak Pata contractions. MJEN. 2022;10(2):228-40.

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