2015, 2015(special): 248-257. doi: 10.3934/proc.2015.0248

Fixed point theorems for cyclic operators with application in Fractional integral inclusions with delays

1. 

Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand, Thailand

Received  August 2014 Revised  May 2015 Published  November 2015

We investigate the existence of fixed points for a very general class of cyclic implicit contractive set-valued operators. We also point out that this class contains an important case of ordered contractions. As an application, we show the solvability of delayed fractional integral inclusion problems.
Citation: Parin Chaipunya, Poom Kumam. Fixed point theorems for cyclic operators with application in Fractional integral inclusions with delays. Conference Publications, 2015, 2015 (special) : 248-257. doi: 10.3934/proc.2015.0248
References:
[1]

A. El-Sayed and A. Ibrahim, Multivalued fractional differential equations, Applied Mathematics and Computation, 68, 1, (1995), 15 - 25.

[2]

A.-G. Ibrahim and A. M. El-Sayed, Definite integral of fractional order for set-valued functions., J. Fractional Calc., 11, (1997), 81-87.

[3]

A. M. El-Sayed and A.-G. Ibrahim, Set-valued integral equations of fractional-orders, Applied Mathematics and Computation, 118, 1, (2001), 113 - 121.

[4]

N. Ahmed and K. Teo, Optimal control of distributed parameter systems. North Holland, 1981.

[5]

N. Ahmed and X. Xiang, Existence of solutions for a class of nonlinear evolution equations with nonmonotone perturbations, Nonlinear Analysis: Theory, Methods & Applications, 22, 1, (1994), 81 - 89.

[6]

Y. Ling and S. Ding, A class of analytic functions defined by fractional derivation., J. Math. Anal. Appl., 186, 2, (1994), 504-513.

[7]

D. Delbosco and L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation., J. Math. Anal. Appl., 204, 2 (1996), 609-625.

[8]

A. Kilbas and J. Trujillo, Differential equations of fractional order: Methods, results and problems. I., Appl. Anal., 78, 1-2 (2001), 153-192.

[9]

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales., Fundamenta math., 3 (1922), 133-181.

[10]

W. Kirk, P. Srinivasan, and P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions., Fixed Point Theory, 4, 1 (2003), 79-89.

[11]

V. Popa, Fixed point theorems for mappings in d-complete topological spaces., Math. Morav., 6, (2002), 87-92.

[12]

I. Altun and H. Simsek, Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory and Applications, 2010, 1, 2010, 621469.

[13]

H. K. Nashine, Z. Kadelburg, and P. Kumam, Implicit-relation-type cyclic contractive mappings and applications to integral equations, Abstract and Applied Analysis, 2012, (2012), 15.

show all references

References:
[1]

A. El-Sayed and A. Ibrahim, Multivalued fractional differential equations, Applied Mathematics and Computation, 68, 1, (1995), 15 - 25.

[2]

A.-G. Ibrahim and A. M. El-Sayed, Definite integral of fractional order for set-valued functions., J. Fractional Calc., 11, (1997), 81-87.

[3]

A. M. El-Sayed and A.-G. Ibrahim, Set-valued integral equations of fractional-orders, Applied Mathematics and Computation, 118, 1, (2001), 113 - 121.

[4]

N. Ahmed and K. Teo, Optimal control of distributed parameter systems. North Holland, 1981.

[5]

N. Ahmed and X. Xiang, Existence of solutions for a class of nonlinear evolution equations with nonmonotone perturbations, Nonlinear Analysis: Theory, Methods & Applications, 22, 1, (1994), 81 - 89.

[6]

Y. Ling and S. Ding, A class of analytic functions defined by fractional derivation., J. Math. Anal. Appl., 186, 2, (1994), 504-513.

[7]

D. Delbosco and L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation., J. Math. Anal. Appl., 204, 2 (1996), 609-625.

[8]

A. Kilbas and J. Trujillo, Differential equations of fractional order: Methods, results and problems. I., Appl. Anal., 78, 1-2 (2001), 153-192.

[9]

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales., Fundamenta math., 3 (1922), 133-181.

[10]

W. Kirk, P. Srinivasan, and P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions., Fixed Point Theory, 4, 1 (2003), 79-89.

[11]

V. Popa, Fixed point theorems for mappings in d-complete topological spaces., Math. Morav., 6, (2002), 87-92.

[12]

I. Altun and H. Simsek, Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory and Applications, 2010, 1, 2010, 621469.

[13]

H. K. Nashine, Z. Kadelburg, and P. Kumam, Implicit-relation-type cyclic contractive mappings and applications to integral equations, Abstract and Applied Analysis, 2012, (2012), 15.

[1]

Yixuan Wu, Yanzhi Zhang. Highly accurate operator factorization methods for the integral fractional Laplacian and its generalization. Discrete and Continuous Dynamical Systems - S, 2022, 15 (4) : 851-876. doi: 10.3934/dcdss.2022016

[2]

Tiziana Cardinali, Paola Rubbioni. Existence theorems for generalized nonlinear quadratic integral equations via a new fixed point result. Discrete and Continuous Dynamical Systems - S, 2020, 13 (7) : 1947-1955. doi: 10.3934/dcdss.2020152

[3]

Hadi Khatibzadeh, Vahid Mohebbi, Mohammad Hossein Alizadeh. On the cyclic pseudomonotonicity and the proximal point algorithm. Numerical Algebra, Control and Optimization, 2018, 8 (4) : 441-449. doi: 10.3934/naco.2018027

[4]

Saima Rashid, Fahd Jarad, Zakia Hammouch. Some new bounds analogous to generalized proportional fractional integral operator with respect to another function. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3703-3718. doi: 10.3934/dcdss.2021020

[5]

Nicholas Long. Fixed point shifts of inert involutions. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1297-1317. doi: 10.3934/dcds.2009.25.1297

[6]

Zhihong Xia, Peizheng Yu. A fixed point theorem for twist maps. Discrete and Continuous Dynamical Systems, 2022, 42 (8) : 4051-4059. doi: 10.3934/dcds.2022045

[7]

Yakov Krasnov, Alexander Kononovich, Grigory Osharovich. On a structure of the fixed point set of homogeneous maps. Discrete and Continuous Dynamical Systems - S, 2013, 6 (4) : 1017-1027. doi: 10.3934/dcdss.2013.6.1017

[8]

Jorge Groisman. Expansive and fixed point free homeomorphisms of the plane. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1709-1721. doi: 10.3934/dcds.2012.32.1709

[9]

Yong Ji, Ercai Chen, Yunping Wang, Cao Zhao. Bowen entropy for fixed-point free flows. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 6231-6239. doi: 10.3934/dcds.2019271

[10]

Shui-Hung Hou. On an application of fixed point theorem to nonlinear inclusions. Conference Publications, 2011, 2011 (Special) : 692-697. doi: 10.3934/proc.2011.2011.692

[11]

Luis Hernández-Corbato, Francisco R. Ruiz del Portal. Fixed point indices of planar continuous maps. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 2979-2995. doi: 10.3934/dcds.2015.35.2979

[12]

Antonio Garcia. Transition tori near an elliptic-fixed point. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 381-392. doi: 10.3934/dcds.2000.6.381

[13]

Mario Ahues, Filomena D. d'Almeida, Alain Largillier, Paulo B. Vasconcelos. Defect correction for spectral computations for a singular integral operator. Communications on Pure and Applied Analysis, 2006, 5 (2) : 241-250. doi: 10.3934/cpaa.2006.5.241

[14]

Marta García-Huidobro, Raul Manásevich. A three point boundary value problem containing the operator. Conference Publications, 2003, 2003 (Special) : 313-319. doi: 10.3934/proc.2003.2003.313

[15]

Cleon S. Barroso. The approximate fixed point property in Hausdorff topological vector spaces and applications. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 467-479. doi: 10.3934/dcds.2009.25.467

[16]

Teck-Cheong Lim. On the largest common fixed point of a commuting family of isotone maps. Conference Publications, 2005, 2005 (Special) : 621-623. doi: 10.3934/proc.2005.2005.621

[17]

Mircea Sofonea, Cezar Avramescu, Andaluzia Matei. A fixed point result with applications in the study of viscoplastic frictionless contact problems. Communications on Pure and Applied Analysis, 2008, 7 (3) : 645-658. doi: 10.3934/cpaa.2008.7.645

[18]

Dou Dou, Meng Fan, Hua Qiu. Topological entropy on subsets for fixed-point free flows. Discrete and Continuous Dynamical Systems, 2017, 37 (12) : 6319-6331. doi: 10.3934/dcds.2017273

[19]

Ruhua Wang, Senjian An, Wanquan Liu, Ling Li. Fixed-point algorithms for inverse of residual rectifier neural networks. Mathematical Foundations of Computing, 2021, 4 (1) : 31-44. doi: 10.3934/mfc.2020024

[20]

Mark S. Gockenbach, Akhtar A. Khan. Identification of Lamé parameters in linear elasticity: a fixed point approach. Journal of Industrial and Management Optimization, 2005, 1 (4) : 487-497. doi: 10.3934/jimo.2005.1.487

 Impact Factor: 

Metrics

  • PDF downloads (99)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]