NEW ASPECTS OF STRONGLY Log-PREINVEX FUNCTIONS
Abstract
In this paper, we consider some new classes of log-preinvex functions. Several properties of the log-preinvex functions are studied. We also discuss their relations with convex functions. Several interesting results characterizing the log-convex functions are obtained. Optimality conditions of differentiable strongly $\log$-preinvex are characterized by a class of variational-like inequalities. Results obtained in this paper can be viewed as significant improvement of previously known results.
Keywords
Full Text:
PDFReferences
G. Alirezaei and R. Mazhar: On exponentially concave functions and their impact in
information theory, J. Inform. Theory Appl. 9(5)(2018), 265-274,
T. Antczak: On (p; r)-invex sets and functions, J. Math. Anal. Appl. 263(2001), 355-
A. Ben-Isreal and B. Mond: What is invexity? J. Austral. Math. Soc. Ser. B,
(1)(1986), 1-9.
S. N. Bernstein: Sur les fonctions absolument monotones, Acta Math. 52(1-66(1929),
-66.
M. A. Hanson: On suciency of the Kuhn-Tucker conditions, J. Math. Anal.
Appl.,80(1981), 545-550.
S. Karamardian: The nonlinear comp-lementarity problems with applications, Part 2,
J. Optim. Theory Appl. 4(1969), 167-181.
G. H. Lin and M. Fukushima: Some exact penalty results for nonlinear programs
and mathematical programs with equilibrium constraints, J. Optim. Theory Appl.
(1)(2003), 67-80.
S. R. Mohan and S. K. Neogy: On invex sets and preinvex functions, J. Math. Anal.
Appl. 189(1995), 901-908.
B. B. Mohsen, M. A. Noor, K.I. Noor and M. Postolache: Strongly convex functions of
higher order involving bifunction, Mathematics, 7(11)(2019):1028.
C. P. Niculescu and L. E. Persson: Convex Functions and Their Applications, Springer-
Verlag, New York, (2018).
K. Nikodem and Z. S. Pales: Characterizations of inner product spaces by strongly
convex functions, Banach J. Math. Anal., 1(2011), 83-87.
M. A. Noor: New approximation schemes for general variational inequalities, J. Math.
Anal. Appl. 251(2000), 217-229.
M. A. Noor: Some developments in general variational inequalities, Appl. Math. Com-
put. 152 (2004), 199-277.
M. A. Noor: Hermite-Hadamard integral inequalities for log-preinvex functions, J.
Math. Anal. Approx. Theory, 2(1)(2007), 126-131.
M. A. Noor: Variational-like inequalities, Optimization, bf 30(1994), 323-330.
M. A. Noor: Invex Equilibrium problems, J. Math. Anal. Appl., 302(2005), 463-475.
M. A. Noor and K. I. Noor: Higher order strongly generalized convex functions, Appl.
Math. Inf. Sci. 14(1)(2020), 133-139.
M. A. Noor and K. I. Noor: Some characterization of strongly preinvex functions, J.
Math. Anal. Appl., 316(2)(2006), 697-706.
M. A. Noor and K. I. Noor: Properties of higher order preinvex functions, Numer.
Algebr. Cont. Optim. 11(3)(2021), 431-441.
M. A. Noor and K. I. Noor: Some properties of exponentially preinvex functions,
FACTA Universitatis(NIS), 34(5)(2019), 941-955.
M. A. Noor and K. I. Noor: New classes of strongly exponentially preinvex functions,
AIMS Math. 4(6)(2019), 1554-1568.
M. A. Noor and K. I. Noor: Strongly log-biconvex Functions and Applications, Earth-
line J. Math. Sci., 7(1)(2021),1-23.
M. A. Noor, K. I. Noor and M. U. Awan: New prospective of log-convex functions,
Appl. Math. Inform. Sci., 14(5)(2020), 847-854.
M. A. Noor, K. I. Noor, A. Hamdi and E. H. El-Shema: On dierence of two monotone
operators, Optim. Letters, 3 (2009), 329-335.
M. A. Noor, K. I. Noor and M. Th. Rassias, New trends in general variational inequal-
ities, Acta Math. Applicandae, 107(1)(2021), 981-1046.
S.Pal and T. K. Wong: On exponentially concave functions and a new information
geometry, Annals. Prob. 46(2)(2018), 1070-1113.
B. T. Polyak: Existence theorems and convergence of minimizing sequences in ex-
tremum problems with restrictions, Soviet Math. Dokl., 7(1966), 2-75.
X. M. Yang, Q. Yang and K. L. Teo: Criteria for generalized invex monotonicities,
European J. Oper. Research, 164(1)(2005), 115-119.
T. Weir and B. Mond: Preinvex functions in multiobjective optimization, J. Math.
Anal. Appl., 136(1988), 29-38.
Y. X. Zhao, S. Y. Wang and L. Coladas Uria: Characterizations of r-Convex Func-
tions, J Optim. Theory Appl. 145(2010), 186-195
D. L. Zu and P. Marcotte: Co-coercivity and its role in the convergence of iterative
schemes for solving variational inequalities. SIAM J. Optim., 6(3)(1996), 714-726.
DOI: https://doi.org/10.22190/FUMI200812058N
Refbacks
- There are currently no refbacks.
ISSN 0352-9665 (Print)