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2021 | OriginalPaper | Chapter

Relative Strongly Exponentially Convex Functions

Authors : Muhammad Aslam Noor, Khalida Inayat Noor, Themistocles M. Rassias

Published in: Nonlinear Analysis and Global Optimization

Publisher: Springer International Publishing

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Abstract

In this paper, we define and consider some new concepts of the strongly exponentially convex functions involving an arbitrary negative bifunction. Some properties of these strongly exponentially convex functions are investigated under suitable conditions. It is shown that the difference of strongly exponentially convex functions and strongly exponentially affine functions is again an exponentially convex function. Results obtained in this paper can be viewed as refinement and improvement of previously known results

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Literature
1.
go back to reference M. Adamek, On a problem connected with strongly convex functions. Math. Inequal. Appl. 19(4), 1287–1293 (2016)MathSciNetMATH M. Adamek, On a problem connected with strongly convex functions. Math. Inequal. Appl. 19(4), 1287–1293 (2016)MathSciNetMATH
2.
go back to reference G. Alirezaei, R. Mazhar, On exponentially concave functions and their impact in information theory. J. Inform. Theory Appl. 9(5), 265–274 (2018) G. Alirezaei, R. Mazhar, On exponentially concave functions and their impact in information theory. J. Inform. Theory Appl. 9(5), 265–274 (2018)
3.
go back to reference H. Angulo, J. Gimenez, A.M. Moeos, K. Nikodem, On strongly h-convex functions. Ann. Funct. Anal. 2(2), 85–91(2011) H. Angulo, J. Gimenez, A.M. Moeos, K. Nikodem, On strongly h-convex functions. Ann. Funct. Anal. 2(2), 85–91(2011)
5.
go back to reference M. Avriel, r-Convex functions. Math. Program. 2, 309–323 (1972) M. Avriel, r-Convex functions. Math. Program. 2, 309–323 (1972)
6.
go back to reference M.U. Awan, M.A. Noor, K.I. Noor, F. Safdar, On strongly generalized convex functions. Filomat 31(18), 5783–5790 (2017)MathSciNetCrossRef M.U. Awan, M.A. Noor, K.I. Noor, F. Safdar, On strongly generalized convex functions. Filomat 31(18), 5783–5790 (2017)MathSciNetCrossRef
7.
go back to reference M.U. Awan, M.A. Noor, K.I. Noor, Hermite-Hadamard inequalities for exponentially convex functions. Appl. Math. Inform. Sci. 12(2), 405–409 (2018)MathSciNetCrossRef M.U. Awan, M.A. Noor, K.I. Noor, Hermite-Hadamard inequalities for exponentially convex functions. Appl. Math. Inform. Sci. 12(2), 405–409 (2018)MathSciNetCrossRef
8.
go back to reference M.U. Awan, M.A. Noor, M.V. Mihai, K.I. Noor, N. Akhtar, On approximately harmonic h-convex functions depending on a given function. Filomat 33(12), 3783–3793 (2019)MathSciNetCrossRef M.U. Awan, M.A. Noor, M.V. Mihai, K.I. Noor, N. Akhtar, On approximately harmonic h-convex functions depending on a given function. Filomat 33(12), 3783–3793 (2019)MathSciNetCrossRef
9.
go back to reference M.U. Awan, M.A. Noor, T.-S. Du, K.I. Noor, New refinements of fractional Hermite-Hadamard inequality. RACSAM 113, 21–29 (2019)MathSciNetCrossRef M.U. Awan, M.A. Noor, T.-S. Du, K.I. Noor, New refinements of fractional Hermite-Hadamard inequality. RACSAM 113, 21–29 (2019)MathSciNetCrossRef
10.
go back to reference A. Azcar, J. Gimnez, K. Nikodem, J.L. Snchez, On strongly midconvex functions. Opuscula Math. 31(1), 15–26 (2011)MathSciNetCrossRef A. Azcar, J. Gimnez, K. Nikodem, J.L. Snchez, On strongly midconvex functions. Opuscula Math. 31(1), 15–26 (2011)MathSciNetCrossRef
12.
go back to reference G. Cristescu, L. Lupsa, Non-Connected Convexities and Applications (Kluwer Academic Publishers, Dordrechet, 2002)CrossRef G. Cristescu, L. Lupsa, Non-Connected Convexities and Applications (Kluwer Academic Publishers, Dordrechet, 2002)CrossRef
13.
go back to reference S.S. Dragomir, I. Gomm, Some Hermite-Hadamard type inequalities for functions whose exponentials are convex. Stud. Univ. Babes-Bolyai Math. 60(4), 527–534 (2015)MathSciNetMATH S.S. Dragomir, I. Gomm, Some Hermite-Hadamard type inequalities for functions whose exponentials are convex. Stud. Univ. Babes-Bolyai Math. 60(4), 527–534 (2015)MathSciNetMATH
14.
go back to reference S. Karamardian, The nonlinear complementarity problems with applications, part 2. J. Optim. Theory Appl. 4(3), 167–181 (1969)MathSciNetCrossRef S. Karamardian, The nonlinear complementarity problems with applications, part 2. J. Optim. Theory Appl. 4(3), 167–181 (1969)MathSciNetCrossRef
15.
go back to reference T. Lara, N. Merentes, K. Nikodem, Strongly h-convexity and separation theorems. Int. J. Anal. 5 (2016). Article ID 7160348 T. Lara, N. Merentes, K. Nikodem, Strongly h-convexity and separation theorems. Int. J. Anal. 5 (2016). Article ID 7160348
16.
17.
go back to reference S.K. Mishra, N. Sharma, On strongly generalized convex functions of higher order. Math. Inequalit. Appl. 22(1), 111–121 (2019)MathSciNetMATH S.K. Mishra, N. Sharma, On strongly generalized convex functions of higher order. Math. Inequalit. Appl. 22(1), 111–121 (2019)MathSciNetMATH
18.
go back to reference C.P. Niculescu, L.E. Persson, Convex Functions and Their Applications (Springer, New York, 2018)CrossRef C.P. Niculescu, L.E. Persson, Convex Functions and Their Applications (Springer, New York, 2018)CrossRef
19.
go back to reference K. Nikodem, Z.S. Pales, Characterizations of inner product spaces by strongly convex functions. Banach J. Math. Anal. 1, 83–87 (2011)MathSciNetCrossRef K. Nikodem, Z.S. Pales, Characterizations of inner product spaces by strongly convex functions. Banach J. Math. Anal. 1, 83–87 (2011)MathSciNetCrossRef
20.
go back to reference M.A. Noor, K.I. Noor, On generalized strongly convex functions involving bifunction. Appl. Math. Inform. Sci. 13(3), 411–416 (2019)MathSciNetCrossRef M.A. Noor, K.I. Noor, On generalized strongly convex functions involving bifunction. Appl. Math. Inform. Sci. 13(3), 411–416 (2019)MathSciNetCrossRef
21.
go back to reference M.A. Noor, K.I. Noor, Exponentially convex functions. J. Orisa Math. Soc. 39 (2019) M.A. Noor, K.I. Noor, Exponentially convex functions. J. Orisa Math. Soc. 39 (2019)
22.
go back to reference M.A. Noor, K.I. Noor, On strongly exponentially preinvex functions. U.P.B. Sci. Bull. Ser. A 81 (2019) M.A. Noor, K.I. Noor, On strongly exponentially preinvex functions. U.P.B. Sci. Bull. Ser. A 81 (2019)
23.
go back to reference M.A. Noor, K.I. Noor, Strongly exponentially convex functions and their properties. J. Adv. Math. Stud. 12(2), 177–185 (2019)MathSciNetMATH M.A. Noor, K.I. Noor, Strongly exponentially convex functions and their properties. J. Adv. Math. Stud. 12(2), 177–185 (2019)MathSciNetMATH
24.
go back to reference M.A. Noor, K.I. Noor, S. Iftikhar, F. Safdar, Some properties of generalized strongly harmonic convex functions. Inter. J. Anal. Appl. 16(3), 427–436 (2018)MATH M.A. Noor, K.I. Noor, S. Iftikhar, F. Safdar, Some properties of generalized strongly harmonic convex functions. Inter. J. Anal. Appl. 16(3), 427–436 (2018)MATH
25.
go back to reference S. Pal, T.K. Wong, On exponentially concave functions and a new information geometry. Annal. Prob. 46(2), 1070–1113 (2018)MathSciNetCrossRef S. Pal, T.K. Wong, On exponentially concave functions and a new information geometry. Annal. Prob. 46(2), 1070–1113 (2018)MathSciNetCrossRef
26.
go back to reference J. Pecaric, F. Proschan, Y.L. Tong, Convex Functions, Partial Ordering and Statistical Applications (Academic Press, New York, 1966) J. Pecaric, F. Proschan, Y.L. Tong, Convex Functions, Partial Ordering and Statistical Applications (Academic Press, New York, 1966)
27.
go back to reference B.T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions. Soviet Math. Dokl. 7, 2–75 (1966) B.T. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions. Soviet Math. Dokl. 7, 2–75 (1966)
28.
go back to reference G. Qu, N. Li, On the exponentially stability of primal-dual gradient dynamics. IEEE Control Syst. Lett. 3(1), 43–48 (2019)MathSciNetCrossRef G. Qu, N. Li, On the exponentially stability of primal-dual gradient dynamics. IEEE Control Syst. Lett. 3(1), 43–48 (2019)MathSciNetCrossRef
29.
go back to reference S. Rashid, M.A. Noor, K.I. Noor, Fractional exponentially m-convex functions and inequalities. Inter. J. Anal. Appl. 17(3), 464–478 (2019)MATH S. Rashid, M.A. Noor, K.I. Noor, Fractional exponentially m-convex functions and inequalities. Inter. J. Anal. Appl. 17(3), 464–478 (2019)MATH
30.
go back to reference D.L. Zu, P. Marcotte, Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities. SIAM J. Optim. 6(3), 714–726 (1996)MathSciNetCrossRef D.L. Zu, P. Marcotte, Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities. SIAM J. Optim. 6(3), 714–726 (1996)MathSciNetCrossRef
Metadata
Title
Relative Strongly Exponentially Convex Functions
Authors
Muhammad Aslam Noor
Khalida Inayat Noor
Themistocles M. Rassias
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-61732-5_16

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